Research Radar.

We study warped compactifications of eleven-dimensional supergravity on eight-manifolds to Minkowski or AdS vacua preserving $N=1$ supersymmetry in three dimensions. For backgrounds characterised by a local G$_2$ structure, we derive an off-shell real superpotential functional in terms of the internal geometry and fluxes without performing a finite Kaluza-Klein truncation. We obtain this expression in two independent ways: from the dimensional reduction of the gravitino variation and from the reduction of the eleven-dimensional gravitino action. We show that the critical-point equations, together with the vacuum value of the superpotential, are equivalent to the full set of supersymmetry conditions implied by the eleven-dimensional Killing spinor equations. When the local G$_2$ structure enhances to a global Spin(7) structure, our result reduces to the known superpotential for M-theory on Spin(7) manifolds.

The supersymmetric index, which gives a signed count of the microstates of black holes, can be computed directly from a gravitational path integral with appropriate boundary conditions. From general arguments based on the supersymmetry algebra, the index is expected to be independent of the temperature and, away from walls of marginal stability, of the asymptotic values of the scalar moduli. On the gravity side, this has been verified by explicit computations in many examples, but a general proof is lacking even at the classical level. We fill this gap by showing that in any four-dimensional supergravity theory with $\mathcal{N} \geq 2$ supersymmetry in asymptotically flat space-time, the classical contribution to the index from each supersymmetric saddle is independent of both. The argument uses only the behavior of the solution and of the Killing spinor equations near infinity. The result therefore holds in the presence of arbitrary higher-derivative corrections and for multi-centered black hole configurations. In particular, moduli independence follows without appeal to the attractor mechanism, which relies on the near-horizon geometry.

The study of continuous spin particles, as general low-energy implications of relativity and quantum mechanics, has intensified in recent years with potential experimental signatures. In this note we show that these particles are absent in perturbative super-string theories, generalising a result in arXiv:1302.4771 to the supersymmetric case. This stands out as a general low-energy prediction of all perturbative superstring constructions.

We study the behaviour of general four-dimensional N=2 supergravity theories near boundaries at infinity of the vector multiplet moduli space, with a focus on a clear distinction between properties that follow from supergravity alone rather than from a consistent UV completion in quantum gravity. The basis for our analysis is the appearance of a real variation of polarised Hodge structure governing the vector multiplet moduli space of N=2 supergravity, combined with very recent advances in the mathematics literature. The resulting classification of infinite distance degenerations exactly agrees, at the level of gauge couplings, with a possible interpretation of the limits as decompactification limits to five or six dimensions or as weakly coupled string limits, as expected from a quantum gravity perspective. This observation extends previous results found in the context of string compactifications on Calabi--Yau varieties and, remarkably, holds for general four-dimensional N=2 supergravity theories regardless of a UV completion. We furthermore show the existence of a Kähler basis in which the triple couplings of the prepotential are non-negative, irrespective of a geometric origin of the supergravity theory. Finally we propose two non-trivial constraints for a four-dimensional N=2 supergravity to be compatible with quantum gravity: Integrality of the Hodge structure as a necessary condition for the completeness hypothesis and the existence of a simple normal crossing compactification of the moduli space to ensure compatibility of the weakly coupled asymptotic gravitational duality frames.

Light scalar fields with gravitational strength interactions (moduli) are ubiquitous in string, supergravity, and extra-dimensional models. If produced in the early universe with lifetimes exceeding the epoch of recombination, slowly decaying moduli inject energetic particles into the Standard Model plasma, leaving distinct imprints on the cosmic microwave background (CMB). In this paper we systematically derive CMB injection bounds on light moduli ($10^3\ {\rm eV}\leq m_{\rm{mod}}\leq 10^8\ {\rm eV}$) across the primary cosmological production channels: vacuum misalignment, heavy scalar/inflaton decay, thermal emission from the primordial plasma including production from a Hagedorn phase of hot strings. We show that these injection bounds impose stringent constraints that are complementary to both the standard cosmological moduli problem and fifth force bounds.

In this work we calculate, for the first time, the dominant perturbative contributions to axion--matter couplings explicitly in string theory. Concretely, we compute these couplings in Calabi--Yau compactifications of heterotic string theory where the vector bundle is a sum of line bundles. They are expressed as overlap integrals requiring the Ricci-flat metric, the Hermitian Yang-Mills bundle metric, and the matter field harmonic forms. We compute these by solving the corresponding coupled differential equations with neural networks. Our results establish a characteristic hierarchy of four-dimensional couplings: axions couple to fermions as $\mathcal{L} \supset c_ψ\,\frac{\partial_μa}{f_a}\, ψ^\dagger \barσ^μψ$ with $c_ψ$ an $\mathcal{O}(1)$ function of Kähler moduli for the model-dependent axions, while the corresponding coupling for the model-independent axion is suppressed by $α_{\rm YM}$ at the ultraviolet matching scale. The model-dependent axions thus couple to fermions similarly as DFSZ-like four-dimensional axions, whereas the model-independent axion's couplings are loop-suppressed as in KSVZ-like constructions. The methods developed here apply directly to the large class of heterotic line bundle models with realistic spectra, and can be adapted to type II constructions.

We present evidence that ten-dimensional type IIB string theory orbifolded by the $\mathbb{Z}_3$ duality symmetry at the strong-coupling fixed point $τ=\exp(2πi/3)$ defines a consistent theory. Motivated by its F-theory dual description and its duality with M-theory in nine dimensions and type IIA string theory in eight dimensions, we argue that the resulting theory is a ten-dimensional chiral non-supersymmetric theory with a discrete gauge symmetry whose bosonic quotient is the automorphism group of the Narain lattice $Γ^{2,2}(A_2)$ ($S_3 \times S_3 \times \mathbb{Z}_2$). We further identify the ten-dimensional tachyon fields with the corresponding Narain moduli. Gauge anomalies cancel nontrivially through a topological Green-Schwarz mechanism involving a $\mathbb{Z}_3$-valued two-form gauge symmetry: the ten-dimensional lift of the familiar zero-form orbifold quantum symmetry in the eight-dimensional type IIA description.

We describe a fully explicit, four-dimensional, top-down de Sitter saddle, constructed via compactification of M-theory on the Riemann-flat manifold $T^7/\mathbb{Z}_8$. The solution has a vacuum energy of $5.02\cdot 10^{-10}\,M_\text{Pl}^4$, a hierarchy $m_{KK}/H\sim 10^{2}$, and is under control with respect to higher-loop and higher-derivative corrections. While the solution is the first example of a top-down dS maximum in four dimensions, it is far from being phenomenologically viable. The solution also suggests several promising directions in the search for higher-quality dS saddles in the Riemann-flat Landscape, which we describe.

Jackiw-Teitelboim (JT) gravity with positive cosmological constant is a toy model to study the emergence of expanding de Sitter universes from a quantum state. Its density matrix is a superposition of double-trumpet amplitudes which are solutions of a Wheeler-DeWitt equation. We compare predictions of such mixed states for classical expanding universes with the corresponding predictions of no-boundary wavefunctions. Double-trumpet amplitudes consistent with holography, whose semiclassical limit matches the result from Schwarzian boundary fluctuations, lead to a flat probability distribution for the size of the universe, consistent with models of inflation. This is in contrast to the suppression of large universes predicted by no-boundary wave functions.

Swampland principles, combined with the smallness of dark energy $Λ$, lead to the dark dimension scenario, with one extra dimension of micron size. We review this scenario and its predictions: KK graviton dark matter (or the KK tower of the quintessence field into which the gravitons convert), neutrino masses tied to $Λ^{1/4}$ via a bulk $B-L$ gauge symmetry, QCD axion decay constant $f_a\sim Λ^{1/12}\sim 10^9-10^{10}$ GeV at the 5d Planck scale $M_5$, connecting electroweak hierarchy to $Λ^{1/6}$, and a relation between the GUT and weak scales with $M_5$ as the geometric mean. The dark dimension also provides a concrete realization of an evolving dark sector: the evolution of its diameter correlates the variation of dark energy with that of the dark matter mass, fitting the recent DESI DR2 (+CMB+supernovae) data while avoiding the phantom crossing that the $w_0w_a$CDM parametrization would suggest---the apparent phantom behavior instead arises from the evolving dark matter mass. The fits suggest that the dark energy field sits in the interior of moduli space, near an unstable critical point. Motivated by this, we review recent progress on non-supersymmetric string vacua: isolated critical points protected by duality symmetries, in non-geometric flux compactifications and in Scherk--Schwarz compactifications of M-theory, and an emerging duality web for non-supersymmetric strings. This note is based on two talks given by the author at String Phenomenology 2026 (Paris) and Strings 2026 (Shanghai).

The flat DHS connection $\mathcal J_{\mathrm{DHS}}$ constructed in arXiv:2602.01461 is smooth on the configuration space of $n$ points on a fixed compact Riemann surface $Σ$ of arbitrary genus $h$, takes values in an infinite-dimensional Lie algebra $\hat{\mathfrak t}_{h,n}$ and is invariant under the modular group $\mathrm{Sp}(2h,\mathbb Z)$. This paper is the first in a series for a program whose goal is to extend the connection $\mathcal J_{\mathrm{DHS}}$ to a global flat connection on the Teichmüller space $\mathcal T_{h,n}$ valued in the Lie algebra of derivations of $\hat{\mathfrak t}_{h,n}$. Upon the choice of local coordinates adapted to the map $\mathcal T_{h,n}\to \mathcal T_h$, such a connection splits into three pieces: $\mathcal J_{\mathrm{DHS}}$, a piece $\mathcal L$ corresponding to holomorphic directions of $\mathcal T_h$ and a third piece corresponding to anti-holomorphic directions in $\mathcal T_h$. In this paper, we isolate the system of equations satisfied by $\mathcal L$ and obtain its solution locally and explicitly. The construction of a global extension of $\mathcal J_{\mathrm{DHS}}$ to $\mathcal T_{h,n}$ and the extension of the meromorphic connection of arXiv:1112.0864 to $\mathcal T_{h,n}$, are relegated to future publications in this series.

We test the Sharpened Distance Conjecture (SharpDC) for CFTs, as well as the Refined Distance Conjecture (RDC), in AdS$_5$ gravitational spacetimes, using the CFT dual. The former provides a lower bound on the exponential mass decay rate of the tower of states becoming light at infinite distance in the conformal manifold, while the latter bounds the bulk field range that can be traversed before the exponential behaviour of the tower kicks in. We prove the SharpDC for any large $N$ Lagrangian supersymmetric gauge theory with a finite number $M$ of gauge factors and vanishing one-loop $β$-function. We also investigate whether it universally holds in the limits of large central charge, finding that it does not: We exhibit concrete examples in Class S theories where the conjecture is violated in the $M\rightarrow\infty$ limit with $N$ fixed, where the size of the bulk internal geometry is much larger than the AdS curvature scale. We also test the RDC in the moduli space of Class S theories without punctures in the large $N$ limit, showing that it amounts to a precise upper bound on the Weil-Petersson diameter of the moduli space of Riemann surfaces of genus $g$. This bound is consistent with all the mathematical literature up to date, but so far remains unproven.

Recently, the possibility of having sterile Majorana neutrinos charged under $B-L$ gauge symmetry in the bulk of the dark dimension has been explored. We point out a cosmological restriction on the Majorana mass of bulk neutrinos leading to mass $\gtrsim 100~{\rm GeV}$. This avoids the over-production of Kaluza-Klein neutrino towers in the early universe thus resolving the cosmological neutrino catastrophe of extra dimension scenarios. If the mass of the bulk neutrino is at the lower end of this bound, it can potentially also explain the recently observed Fermi halo excess on gamma rays through the evaporation of long-lived 5d (i.e. dark) black holes through Hawking radiation to bulk neutrinos, which promptly decay into standard model particles.

We initiate a systematic cosmological investigation of an axio-dilaton system governed by a curved field-space metric as generically motivated by supergravity and string compactifications. The scalar sector consists of a light scalar dilaton field evolving along an asymptotically exponential potential and a pseudoscalar field spanning an essentially flat direction, kinetically coupled through an exponential field-space metric. Deviations from the asymptotic regime are incorporated by introducing a generalised Albrecht-Skordis potential containing a polynomial factor. Utilising a dynamical systems approach alongside numerical evolution and Bayesian inference, we constrain the model using Type Ia Supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO) and Planck 2018 distance-prior data. We identify a parameter degeneracy indicating that steeper potentials demand stronger field-space kinetic couplings to sustain late-time cosmic acceleration. Finally, a joint likelihood analysis reveals that while the model successfully accounts for dark energy dynamics, it is only slightly statistically favoured over $Λ$CDM by current observations.

We present a suite of 50 unpublished research-level theoretical physics problems with verifiable answers. Without AI assistance, a typical problem in our collection could be solved by a world expert in about a day or less but would take considerably longer for experts in adjacent specialties. We test the ability of off-the-shelf AI agents to tackle these problems autonomously, without human hints. When given access to tools available in a realistic setting, including the ability to search the literature and write scripts for numerical and symbolic work, the best-performing agent, GPT-6-Astra harnessed in Codex, obtains the final answers with a near-perfect accuracy of 98% at an average cost under USD 3 per problem. On average, agents show only small changes in accuracy when denied web search and access to background research papers, suggesting significant memorization of the literature. These results suggest that state-of-the-art agents can accurately perform concrete calculations required across theoretical physics research. We comment on the broader implications of these findings and discuss possible explanations for the current lack of agent-led breakthroughs in theoretical physics despite their outstanding problem-solving abilities.

Massive spin 2 fields on de Sitter must satisfy the Higuchi bound, $m^2\geq 2H^2$. Compactifications of higher dimensional gravity to $\mathrm{dS}_4$ come with a tower of Kaluza-Klein gravitons whose masses are fixed by the internal geometry, so the bound becomes a constraint on the compactification. We propose that the KK gravitons of a consistent compactification never violate it, and test this in a few examples. On a circle stabilized by Casimir energy the bound holds unless the circle shrinks below the species scale, and on a warped interval with negative tension branes the tower is gapped at $m^2\geq \tfrac{9}{4}H^2$ for any length of the interval. On group manifolds, we argue that if the internal curvature is not parametrically larger than the Hubble scale, the bound can apparently be violated by smooth deformations. The violation disappears once one promotes these deformations to moduli, which are immediately extremized when solving the 10d equations of motion.

The classical soft graviton theorem aims to determine certain terms in the early- and late-time tails of the gravitational waveform produced in a scattering process, using only the asymptotic momenta of the scattered objects. In this paper we find an infinite series of leading-logarithmic tail terms in the Newtonian limit, where the incoming and outgoing particles move slowly, but the scattering itself can be violent. The all-orders conjecture of Alessio, Di Vecchia and Heissenberg agrees with our results for two-particle scattering, but does not hold in general when the initial or final state contains three or more particles. We also propose an all-orders conjecture for these tails beyond the Newtonian limit, but do not prove it. Nevertheless, the conjecture passes several nontrivial consistency checks.

After re-examining a classic article by Hugh Everett, I will discuss the entropy of de Sitter space from the standpoint of an observer living in the space. This provides a nice example of the importance -- for certain questions -- of taking seriously the fact that in cosmology any observer is really part of the universe that is being observed. (This article has appeared in a special issue of International Journal of Modern Physics A in honor of Gerard 't Hooft.

In the context of the AdS/CFT correspondence, the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula relates the boundary modular Hamiltonian to the HRT area operator and the corresponding bulk modular Hamiltonian. In standard discussions of a holographic code built from perturbative excitations on a fixed classical background, the $A/4G$ term dominates over the bulk modular Hamiltonian in the limit $G \to 0$. However, this setup is insufficient to describe the action of boundary modular flows that change the classical background. In contrast, our recent discussion of `large' codes provides a useful framework to obtain a JLMS formula that relates bulk and boundary modular flows acting on appropriate states in the code. Here, one sees that the bulk modular Hamiltonian is not in fact subdominant when the modular flow defined by one state acts on another state peaked around a sufficiently different classical background. Instead, the bulk modular Hamiltonian can be of order $1/G$ and can dominate over the $A/4G$ term. Nevertheless, we show that if the two states have the same classical background except for data conjugate to the HRT area then, under mild assumptions and over a large range of flow parameters, the modular-flowed state is described by a classical background given by the HRT-area flow alone.

We study the invertible one-form global symmetry of a (2+1)-dimensional topological quantum field theory (TQFT). A universal description of this symmetry ``peels off'' all the Abelian anyons from the rest of the TQFT. This allows us to study this symmetry and some of its consequences, independently of the details of the rest of the system. We then describe these Abelian anyons using $\mathrm{U}(1)$ gauge fields with Chern-Simons terms and couple them to a scalar field, thus constructing a particular non-topological theory. This new theory, our transition field theory, exhibits a phase transition from the original TQFT to another phase. The latter is either gapless or another TQFT. This discussion generalizes and extends our earlier work (arXiv:2603.00245). In particular, we give a more detailed description of the global symmetries and their fates in the various phases.

We study the entanglement structure of partially entangled thermal states in double-scaled SYK , allowing flavor degrees of freedom carried by matter insertions to be in an arbitrary mixed state. In the semiclassical limit, followed by the heavy-probe limit, our replica calculation gives a Faulkner--Lewkowycz--Maldacena formula: the boundary entropy decomposes into an `area' term (independent of the flavor state) and the bulk matter entropy in a corresponding entanglement wedge. Varying the Euclidean locations of the operator insertions produces sharp transitions in the boundary entropy, which we interpret as individual matter excitations crossing the boundary of the wedge and hence as evidence for a sharply defined entanglement wedge. To derive this result, we analyze the semiclassical behavior of general Euclidean $2n$-point functions and give a probabilistic proof of their factorization into sums over products of two-point functions. We also give a complementary derivation from exact spectral representations, using the semiclassical behavior of the quantum $6j$-symbol.

We develop a bootstrap approach for weakly broken gauge theories in (anti-)de Sitter space, focusing on cases in which the conservation of the dual boundary current is broken by a double-trace operator. Integrating the corresponding Ward identity, we derive pseudo-charge conservation identities that contain fixed nonlocal contributions as integrals of three-point functions. These identities impose consistency conditions on the space of allowed theories. As an illustrative example, we study Yang-Mills theory in AdS with symmetry-breaking boundary conditions for charged matter and show that the pseudo-charge conservation identities constrain the mixing between the two quantization sectors. We then apply the framework to the Higgs mechanism for gravity in two AdS spaces with a common boundary, coupled so that the corresponding stress tensors are not separately conserved. In this setting, the ordinary charge conservation identities recover the factorization into two independent CFTs, whereas the pseudo-charge conservation identities hold for arbitrary values of the symmetry-breaking parameter. Finally, for conformal gravity in de Sitter space, we constrain the interactions between the graviton and the partially massless spin-2 field, both in the minimal theory and in the presence of additional scalar or vector matter, finding agreement with the predictions of the corresponding bulk theories.

We study the inflationary no-boundary wavefunction in a ``linear-roll limit,'' in which $G_N \to 0$ while the Hubble scale $H$ and the slope of the inflaton potential are held fixed. Although bulk graviton fluctuations are suppressed in this limit, quantum inflaton fluctuations remain finite. Because reheating occurs on a surface of fixed inflaton value, these fluctuations become fluctuations of the conformal factor of the reheating metric. The probability measure for these fluctuations simplifies drastically and becomes Gaussian, even for large fluctuations. The resulting log-correlated theory at superhorizon scales is a $d$-dimensional analog of Liouville gravity without the exponential potential, which we call Logarithmic Gravity. The quadratic and linear terms are determined by conformally covariant scattering data; in even dimensions we relate them to the critical GJMS operator and Branson $Q$-curvature. From bulk unitarity, we argue that one-loop effects do not generate additional conformal-factor dependence in the physical probability measure, and we verify the cancellation explicitly in $2 + 1$ dimensions. For the no-boundary norm with a rolling inflaton, we show that the noncompact residual conformal symmetries can be gauge fixed with a finite Faddeev-Popov determinant, so they do not force the sphere contribution to vanish. In addition, conditioning on the absence of vacuum decay by bubble nucleation generates the Liouville exponential potential in the probability measure.

The African School of Fundamental Physics and Applications, also known as the African School of Physics (ASP), was initiated in 2010, as a three-week biennial event, to offer additional training in fundamental and applied physics to African students with a minimum of three-year university education. Since its inception, ASP has grown to be much more than a school. ASP has become a series of activities and events to support academic development of African students, teachers, high school pupils (learners) and faculties. We report on the ninth African School of Physics, ASP2026, organized in Kenya, on July 5--19, 2026. ASP2026 included programs for university students, high school teachers and learners.

We derive the axion Weak Gravity Conjecture (aWGC) from the nonperturbative fragmentation of Euclidean wormholes into charged defects. Requiring fragmentation to lower the Euclidean action fixes the axion action-to-charge bound and its order-one coefficient. Without additional scalars, this coefficient coincides with that of the Imaginary Distance Bound (IDB), while additional scalars strengthen the bound. The aWGC in the presence of multiple axio-dilaton pairs is discussed, leading to geometric representations. Axions satisfying the aWGC render the corresponding wormholes unstable, potentially suppressing their proliferation and resolving associated factorization problems.

The gravity approximation to a thermal two-point function can develop a complex-time singularity associated with a trajectory that reaches the black-hole singularity. We show that the corresponding singularity is absent at finite $G_N$. This is done by extending Conformal Field Theory analyticity properties to the second sheet (and to the universal cover). We also put two different upper bounds on the amplitude of the correlator at the would-be singularity, by certain finite partial sums, and by a certain partition function on a manifold with nontrivial topology, where two thermal geometries are glued. We discuss the possible implications for the black hole singularity.

In infinite-distance limits of scalar field moduli spaces in quantum gravity, particle masses, brane tensions, and scalar field potentials scale exponentially with geodesic distance. Previous work has shown that the exponential decay rates of particle masses and brane tensions admit a discrete classification. In this work, we extend this classification to the case of scalar field potentials. We find that leading contributions to the potential typically scale with tensions of codimension-1 branes as $V \sim T_{d-1}^2$ or codimension-0 branes as $V \sim T_d$, and these relations hold formally even when the associated branes are absent from the spectrum. As a result, the taxonomy rules for potentials are intimately connected to the brane taxonomy rules. More generally, potential contributions can be labeled by a collection of integers, which correspond physically to their transformation properties under Weyl rescalings and their order in the string loop expansion. This implies that the vector $\vec v = - \vec \nabla \log V$ is lattice-valued, and indeed it lies in precisely the same lattice as the analogous vectors $\vec α= - \vec \nabla \log T_d$ for codimension-0 branes of tension $T_d$. We verify our taxonomy rules in various examples in string theory. We show that these rules imply that sums of positive potential terms satisfy the Strong Asymptotic de Sitter Conjecture, which requires $|\vec \nabla \log V| \geq 2/\sqrt{d-2}$ in asymptotic regimes of scalar field moduli space, and they imply that higher-derivative gravitational corrections are suppressed by powers of the species scale.

We revisit the long-standing problem of the anyon gas. We study the solvable near-bosonic limit of a large number of anyons $N$ at fixed $N/k$, where $1/k$ characterizes the statistical interaction. In this limit, the ground state is a crystal with order $N/k$ lattice sites. The statistical interactions, mediated by a long-range gauge field, are completely screened within the crystalline phase. The resulting state is a conventional crystal without superfluidity. We characterize this anyon crystal by determining its unit-cell size, ground-state energy, acoustic excitations, angular momentum crossings, and other properties. Our results indicate a quantum phase transition between the crystal at $k>k_c$ and a superfluid at $k<k_c$, with a critical value $k_c\simeq2\text{--}5$. These results imply that an anyon gas with only statistical interactions is not necessarily a superfluid, contrary to common lore. We also present a detailed analysis of the renormalization-group evolution of anyon--anyon interactions, identifying many new potential fixed points and elucidating finite-size effects.

We present a maximally supersymmetric extension of the BFSS matrix model based on the 5-Lie algebra ${\mathcal A}_6$. The theory is Lagrangian, promotes the BFSS 2-bracket structure constants to dynamical objects governed by a Chern-Simons-like kinetic term, and displays features expected from a theory of M5-branes. We show that it can also be obtained from the single lightcone M5-brane action on a spatial five-sphere after a truncation to the time coordinate. The resulting theory is a consistent truncation and, analogously to the $U(2)$ BFSS model, supports an interpretation of the $\mathcal{A}_6$ theory as a quantum-mechanical model for the lowest-lying modes of the M5-brane.

In this article, I will define the Chern-Simons invariant of a gauge connection over a three-manifold and explain some of the things that are special about it, in particular its role in understanding the quantum Hall effect, which is an important effect in condensed matter physics, and its generalization, the fractional quantum Hall effect. (The article is based on a lecture at a conference celebrating the 75th birthday of James Simons, held at the CUNY Graduate Center in 2013. It will appear in the Bulletin of the American Math Society.

The $n$-point single-minus graviton amplitudes are nonzero in a special kinematic region that preserves some supersymmetry when embedded in supergravity. We compute these amplitudes within the BFSS matrix theory by relating them to an index problem considered by A. Sen. More precisely, the single-minus amplitudes are obtained from an index that counts BPS states in the Coulomb branch of four-dimensional ${\cal N}=4$ super Yang-Mills. We explicitly check this relation in a specific kinematic region by computing the index using BPS wall-crossing formulae and matching it to the gravity result. We further employ BPS wall-crossing to show that the index satisfies a tower of $w_{1+\infty}$ soft theorems in any kinematic regime, again matching gravity. Finally, we show that for certain kinematics, the single-minus amplitudes can be realized by scattering a graviton off a plane wave.

We study the quantum dynamics of supersymmetric Galilean Yang-Mills (SGYM), with a focus on three dimensions where there is a classical scale symmetry. This is believed to be the worldvolume theory describing D2-branes within type IIA non-relativistic string theory and arises as a non-relativistic limit of maximally supersymmetric (relativistic) Yang-Mills. Unlike the relativistic case, we find that SGYM only admits perturbative dynamical excitations on the Coulomb branch. We show that in three dimensions the classical scale symmetry is broken at one-loop due to logarithmic divergences. These cannot be regulated without introducing additional marginal deformations, and we present evidence that the theory is asymptotically free once these are included. In particular our analysis suggests that three-dimensional SGYM flows to a strongly coupled non-relativistic M2-brane theory.

We initiate a systematic study of compactifications of type II string theory to two dimensions on Ricci-flat spaces with fluxes and sources. We derive universal constraints on such compactifications, and then develop type IIA compactifications on $\mathrm{Spin}(7)$-holonomy spaces with bulk fluxes whose tadpole is cancelled by $\mathrm{OF1}$-planes. We derive the resulting two-dimensional $\mathcal N=(1,1)$ supergravity for a toroidal $\mathrm{Spin}(7)$ orbifold, and we extend the metric and universal sectors geometrically to general compact $\mathrm{Spin}(7)$ manifolds. In candidate supersymmetric Minkowski vacua, all untwisted shape modes appear in the flux scalar potential and can in principle be classically stabilised. However, in an explicit toroidal orbifold example flux quantisation together with the tadpole bound may obstruct the existence of candidate vacua supported entirely within the untwisted sector. The string-frame volume in string units is bounded by $7χ/192$, so suppressing $α'$ corrections requires $\mathrm{Spin}(7)$ manifolds with large Euler characteristic.

The Weak Gravity Conjecture admits a formulation in terms of long-range charged particle self-interactions being repulsive. We adopt a similar approach to the Axionic Weak Gravity Conjecture by considering long-range instanton interactions. At leading order, in the instanton separation, such interactions are mediated purely by massless scalar fields. Gravitational and gauge interactions are sub-leading. We formulate a repulsive interaction Axionic Weak Gravity Conjecture, which forms a bound on the scalar field dependence of the complex Euclidean instanton action. We show that in standard ultraviolet complete examples, this bound implies the usual formulation of the Axionic Weak Gravity Conjecture, while generally being stronger. Because this formulation is purely a statement about massless scalar fields, it implies that in the absence of massless scalars the usual bound on the axion decay constant could be modified.

Einstein gravity in four asymptotically flat dimensions is governed by a tower of soft theorems obeying an $\mathcal{L}w_{1+\infty}$ commutator algebra. This algebra is deformed to $\mathcal{L}_Λw_{1+\infty}$ in the conformally related AdS$_4$ and dS$_4$ spacetimes. Here we construct the larger ``conformal $w$-algebra", denoted $\mathcal{C}w_{1+\infty}$, which acts on conformal gravity in all of these spacetimes. It includes $\mathcal{L}w_{1+\infty}$, $\mathcal{L}_Λw_{1+\infty}$ and the $\mathfrak{so}(4,2)$ 4D conformal algebra as subalgebras. We show that $\mathcal{C}w_{1+\infty}$ is the conformal completion of either $\mathcal{L}w_{1+\infty}$ or $\mathcal{L}_Λw_{1+\infty}$. A derivation of $\mathcal{C}w_{1+\infty}$ is given as the symmetry of the twistor action of self-dual conformal gravity.

We describe a large class of theories that continuously interpolate between single and double trace $T\bar T$ deformations of AdS$_3$/CFT$_2$. It is obtained by starting with the spacetime $M_3$, which interpolates between AdS$_3$ in the IR and a linear dilaton spacetime in the UV, and imposing a UV cutoff on the radial direction. When the cutoff is deep in the AdS$_3$ region of $M_3$, this leads to double trace $T\bar T$. When it goes to infinity, we recover the single trace deformed theory. We present a large class of possible boundary conditions on the dilaton, and compute the resulting black hole spectrum in a few examples. In all these constructions, to leading order in the low energy expansion, the resulting spectrum is that of a single $+$ double trace deformed CFT, but at higher orders the different theories have different spectra. In one of the examples that we analyze, the full theory is single $+$ double trace $T\bar T$ deformed CFT. Another gives rise to an interesting spectrum, that consists of an infinite set of energy bands.

Higgsino dark matter is a classic, but still viable, weakly-interacting massive particle (WIMP) scenario that could point to supersymmetry, a new spacetime symmetry of nature. It is a simple realization of the "inelastic dark matter" mechanism, where its scattering off a nucleus occurs between two nearly degenerate states. Intriguingly, very recently the LZ collaboration reported a single nuclear recoil event at a high recoil energy. Assuming that this event is a dark matter candidate, it could be explained by higgsino dark matter, e.g., a 1.1 TeV thermal higgsino with a mass splitting of order hundreds of keV. The mass splitting required is very sensitive to the extreme high speed tail of the local dark matter velocity distribution, and thus susceptible to astrophysical uncertainties: the standard halo model prefers ~350 keV, while a model incorporating Large Magellanic Cloud effects prefers ~500 keV (a rough estimate based on partial information about a particular simulation). A much better understanding of the high speed tail is needed to evaluate whether the parameter space is consistent with an IceCube constraint on the annihilation of dark matter captured by the Sun. In any case, the mass splitting of several hundred keV implies that the electroweak gauginos and heavy Higgs scalars in supersymmetry have to be at a much higher scale ~10^{3-4} TeV. We discuss possible UV completions to generate a SUSY spectrum in which all superpartners are at a common scale, except for a much lighter higgsino mass $μ$. Besides the thermal benchmark, we comment on possible non-thermal cosmological scenarios of higgsino dark matter with gravitino and modulus decays. The higgsino dark matter scenario could also be searched for at other complementary probes such as indirect detection and future colliders. One striking LZ event may herald an exciting future of further experimental developments.

Quantum Yang-Mills theory in Euclidean AdS$_4$ with Neumann boundary conditions is studied as a function of the complex couplings $\frac{1}{g_\pm^2} \equiv \frac{1}{g^2}\mp \frac{i θ}{8 π^2}$. We define a "self-dual limit" by $g_- \to 0$ with $g_+ ~{\rm fixed}$. We argue that the limiting theory is well-defined perturbatively and equivalent to the BF formulation of self-dual Yang-Mills theory with a particular boundary condition relating $B$ and $F$ at the boundary $\partial$AdS$_4$. $g_+$ is the loop-counting parameter of the self-dual theory. This is in stark contrast to flat space, where $θ$ has no effect on perturbative dynamics. In the self-dual limit, it is shown that all tree-level zero-plus and single-plus boundary correlators vanish. A closed form expression is given for any number of gluons for the double-plus tree correlators. Finally, we show that in the flat space limit of AdS$_4$, the total energy poles in the tree boundary correlators correctly reduce to the single-minus gluon amplitudes.

Motivated by inflation and Liouville theory, we consider random $d$-dimensional geometries characterized by an overall scale factor $ds^2 = e^{2 ζ} dx^2 $ given in terms of a random Gaussian field $ζ(x)$ with logarithmic correlations. We discuss aspects of the renormalization of the volume element $e^{d ζ}$, connecting well-known Liouville theory formulas (KPZ) and inflationary ones. By starting from a fixed physical cutoff and coarse-graining operators to a fixed fiducial cutoff, defined via the flat metric $dx^2$, we provide a direct physical derivation of the KPZ scaling relation. We point out that the same renormalization problem arises in stochastic inflation, where it is modeled by Brownian motion of the inflaton field. We show that the breakdown of the renormalization of the Liouville volume when the fluctuation amplitude exceeds a critical value corresponds to the transition to eternal inflation. In $d = 2$, this matches the familiar $c_m = 1$ barrier in Liouville gravity. We also discuss connections to mathematical probabilistic approaches to random surfaces.

The Hadamard maximal determinant problem seeks an $n\times n$ matrix $X$ with entries in $\{\pm 1\}$, which maximizes the determinant $\vert \det X \vert$ for a given order $n \in \mathbb{N}$. We report matrices attaining new record determinants for orders $n\equiv 3\pmod{4}$ between $103$ and $119$, as well as $n=51$. We provide a proof of optimality within a specific family of circulant--block constructions for $X$. For these orders, we recast the Hadamard problem as a sequence reconstruction problem from a pair of periodic autocorrelation functions, subject to certain arithmetic conditions. We describe several learning--based strategies for reconstruction and provide a comparison with classical simulated annealing--style approaches as a benchmark.

Quintessential $α$-attractor models of single-field inflation and evolving dark energy were constructed about a decade ago. Recently, it was pointed out that some of them might be disfavored due to dark-radiation constraints on gravitational waves and the higher values of $n_s$ favored by ACT. Here we present a class of updated quintessential $α$-attractor models in which a single field describes both inflation and evolving dark energy, yields higher values of $n_s$, and admits reheating scenarios consistent with the dark-radiation bound on $ΔN_{\rm eff}$. Depending on the value of the cosmological constant $Λ$, these models interpolate between $Λ$CDM with $Λ> 0$ (future dS universe), dynamical dark energy with $Λ= 0$ (future Minkowski universe), and dynamical dark energy with $Λ< 0$ (future cosmological collapse). We also study quintessential $α$-attractor models based on an axion-inflaton complex scalar field with hyperbolic geometry, which describe inflation and dark energy of a ``phantom illusion'' type compatible with DESI DR2.

Machine learning and data analysis techniques have recently emerged as powerful tools for identifying patterns and formulating conjectures in mathematical research, most notably in the field of low-dimensional topology. In this paper, we initiate a systematic approach to handling mathematical data structured as (truncated) infinite $q$-series, or equivalently, infinite series of integers. To apply this data analysis pipeline, we construct a comprehensive dataset of $\widehat{Z}$-invariants (homological blocks) for plumbed 3-manifolds. We demonstrate that neural networks can reliably extract essential topological information, such as homology class and underlying graph structure, directly from the $q$-series coefficients. A central feature of our methodology is a focus on interpretability; by contrasting local gradient sensitivity with global feature relevance, we reveal that the networks learn to bypass complex topological rules in favor of specific spectral and geometric proxies. Finally, we apply this pipeline to probe homology cobordism, discovering a high-accuracy predictive relationship between the $\widehat{Z}$-invariant exponents and the Heegaard Floer $d$-invariant (correction term). These results suggest that $\widehat{Z}$-invariants capture subtle geometric information regarding cobordism equivalences, warranting a new direction for the study of quantum invariants.

We study aspects of the Euclidean partition function of the $\frac{SL(2,\mathbb R)\times U(1)}{U(1)}$ gauged WZW model. The target space geometry is either a smooth horizonless geometry with a linear-dilaton asymptotic region, or the Horne--Horowitz black string, depending on which circles we unwind as the time-direction. We first study the worldsheet spectrum and obtain the character decomposition via the holonomy integrals. Next, we obtain the spacetime spectrum of the horizonless geometry by directly performing the unfolded modular integrals, and recover the Maldacena-Ooguri-Son spectrum in the ungauged limit. When the chirally charged three-dimensional black string is dimensionally reduced, the target space is instead a two-dimensional charged black hole. We study the near extremal regime of the black hole and black string. For the two dimensional black hole, we propose two candidate towers of states that produce the expected $\frac{3}{2}\log T$ of the AdS$_2$ throat from the worldsheet discrete series representation. These towers appear only below the temperature at which the full amplitude becomes divergent. We comment on the contribution of these states in the near-extremal limit of the full partition function.

We take a first step in identifying the superconformal quantum mechanics dual to supersymmetric AdS$_2\times$S$^2$ solutions. We focus on the Type IIB solutions of the form AdS$_2\times$S$^2\times$CY$_2\timesΣ$ that preserve eight supercharges, with $Σ$ a two-dimensional space parametrised by $(x_1,x_2)$, and read off their brane content, a D1-D5-NS5 intersection with D3 and D7 flavour branes. We propose that their dual $\mathcal{N}=4$ quantum mechanics is organised over a two-dimensional lattice of cells in $Σ$. Namely, it consists of copies of the linear quiver along $x_1$ dual to the U(1)-invariant solutions of the class, one for each interval along $x_2$, with ranks given by the D1 and D5 charges of the corresponding cell. Its central charge agrees with the holographic one at leading order. We show that the family of SL$(2,\mathbb{R})$ non-Abelian T-duals of the AdS$_3\times$S$^2\times$CY$_2$ solutions of massive Type IIA supergravity, constructed in previous work, belongs to this class, as does the SL$(2,\mathbb{R})\times$SU$(2)$ non-Abelian T-dual of AdS$_3\times$S$^3\times$CY$_2$, and work both out in detail. For both we propose global completions that introduce additional D3 and D7 branes. Along $x_2$ we interpret the fundamental strings stretched between the colour branes and the additional D3 and D7 branes as baryon vertices. Finally, we extend this proposal from the non-Abelian T-duals to the solutions of the class whose defining functions factorise in $x_1$ and $x_2$, including those in which the AdS$_2$ and S$^2$ factors have the same warp factor.

We investigate the early-universe cosmological implications of Unimodular Gravity coupled to Power-Law Nonlinear Electrodynamics in the presence of quantum-corrected horizon thermodynamics derived from the principle of thermodynamic duality. By incorporating both logarithmic and inverse-area corrections to the Bekenstein-Hawking entropy, we derive modified Friedmann equations exhibiting novel $H^4$ and $H^6$ terms that represent genuine quantum gravity effects. We demonstrate that these higher-order corrections become dynamically significant in the high-energy regime of cosmic inflation, naturally modifying the slow-roll dynamics without requiring a fundamental inflaton potential. A comprehensive phase-space analysis reveals that the quantum corrections drive early-time de Sitter-like attractors, providing a robust mechanism for sustained inflationary expansion. Confronting the model with the Swampland program, we show that the correction factor $\mathcal{F}(H)$ modifies the effective slow-roll parameters, enabling the model to satisfy the Swampland de Sitter and Distance conjectures during the inflationary epoch. We calculate the inflationary observables, including the spectral index $n_s$ and the tensor-to-scalar ratio $r$, and demonstrate that the model's predictions are in excellent agreement with the Planck 2018 observational constraints. Our results suggest that thermodynamic duality-induced horizon corrections offer a viable and testable pathway for realizing successful inflation within a well-motivated quantum-gravitational framework.

Via the Rindler method, we study holographic timelike entanglement entropy (TEE) for a general timelike interval in AdS$_3$/CFT$_2$ and flat$_3$/CCFT$_2$. The TEE is the pseudo entropy of a timelike interval. In the bulk, the imaginary part of the TEE comes from a timelike geodesic, but in the Rindler picture this geodesic has not been identified. After a Rindler transformation to a rotating BTZ black hole, the two spacelike extremal curves lie on the inner and outer horizons, and exchanging $l_u\leftrightarrow \ell l_φ$ takes one to the other. We find the geometric meaning of the timelike extremal curve: a geodesic stretched between the two horizons. Its length, $iπ\ell$, is independent of the interval, and it alone produces the imaginary part $iπc/6$. We follow the same procedure in flat space holography, where the spacelike curve sits on the cosmological horizon and the timelike curve lies between the cosmological horizon and timelike infinity. Evaluating the holographic TEE for a timelike interval in CCFT$_2$ on the plane, we find that, in contrast with the cylinder, the real and imaginary parts are equal.

Timelike entanglement entropy provides a useful probe of holographic theoris, yet an explicit bulk realization of the modular flow underlying its timelike extremal curve construction has so far been lacking. We construct modular flows associated with spacelike and timelike intervals in AdS$_{3}$/CFT$_{2}$ and extend this framework to flat$_{3}$/CCFT$_{2}$. Beginning with the boundary symmetry generators, we explicitly derive the boundary modular flows and extend them into the bulk, providing a systematic procedure that relates bulk modular flows to the extremal curves and holographic (timelike) entanglement entropy. For spacelike intervals, the resulting bulk modular flows determine the extremal curves, whose integrated line elements reproduce the standard holographic entanglement entropy. We then generalize this approach to timelike intervals, explicitly constructing the modular flows whose fixed points reproduce the extremal spacelike and timelike curves which gives the holographic timelike entanglement entropy. To the best of our knowledge, this is the first explicit construction of the modular flow associated with a timelike extremal curve for a timelike interval. The same procedure is then carried over to flat$_{3}$/CCFT$_{2}$, which give rise to the holographic (timelike) entanglement entropy. Finally, we show that the flat space results obtained in this work can be recovered from their AdS$_3$ counterparts in the flat space limit.

We study the imaginary part of the holographic timelike entanglement entropy (HTEE) in a charged asymptotically AdS$_5$ black-hole background whose dual field theory exhibits a critical point in the presence of a chemical potential $μ$ and temperature $T$. Identifying the imaginary part of the HTEE with the imaginary part of the pseudoentropy, we derive an analytical expression for this quantity and investigate its behavior on the stable and unstable thermodynamic branches. We find that the imaginary HTEE vanishes in the uncharged limit and is induced entirely by a nonzero chemical potential, signaling the emergence of quantum coherence between the initial and final states. As the dimensionless ratio $μ/T$ approaches its critical value, we obtain an inverse-square-root divergence in the derivative of the imaginary HTEE and extract the critical exponent $θ_I = 1/2$ analytically. We further show that the same exponent governs the temperature response at fixed chemical potential. Our results establish the imaginary part of the HTEE as a non-local quantum-information probe of criticality in strongly coupled systems, and they imply that the initial and final states become maximally coherent at the critical point.

The Okubo algebra brings together ternary gradings, integral root frames and rank-three geometry. We examine how these structures extend to the complex Exceptional Periodicity algebras. With $N=4(n+1)$, a tetracode character gives eight nonzero homogeneous components of dimension $t_n=8n+3+2^{4n}$. On a tip, a compatible grading has zero component of dimension $8n-5$ and eight nonzero components of dimension $1+2^{4n-3}$. The arithmetic behaves differently: for $n\geq2$, the lattice $D_N^+$ has no full-rank orthogonal frame of unscaled $A_2$ lattices. We exhibit failures of the Jacobi and Jordan identities and determine the derivations and full automorphism group of the ambient algebra above level one. We also give a Clifford-module proof, with the normalization fixed by root products, of the published realization of EP tips as special Vinberg $H$-algebras. This identifies a positive real form and yields explicit formulas for its cone, cubic, Cholesky coordinates and rational dual invariant. The cone is symmetric exactly at $n=1$. Its determinant-one hypersurface belongs to the known $L(8n,1,0)$ series, whose $r$- and $c$-maps give homogeneous scalar manifolds for supergravity theories with eight real supercharges.

We construct a three-parameter family of regular analytic supergravity solutions which are dual to (a) the $\mathcal{N}=2^*$ gauge theory on the four-sphere, and (b) $\mathrm{U}(1)^2$-invariant Janus interfaces in $\mathcal{N}=4$ SYM with or without the $\mathcal{N}=2^*$ mass turned on. To this end we employ a five-dimensional supergravity model coupled to six scalars which arises as a certain consistent truncation of type IIB supergravity on $S^5$. The curved domain wall solutions feature a hidden integral of motion which allows for their analytic treatment. We relate the three parameters of the solution to field theory sources and vevs and show how regularity of the solutions restricts their range. We briefly discuss the holographic evaluation of the one-point function of the field theory Lagrangian for our family of Janus solutions.

Modifications of gravity beyond (vacuum) General Relativity have a subtle impact on the physics around black holes. Describing these effects across different observables is, however, a priori strongly model dependent. While effective descriptions of the geometry allow to efficiently capture deviations from benchmark predictions, they sometimes lack a clear passage towards (effective) new physics. Inspired by linear response theory, in this work I therefore propose a formalism that allows to calculate leading corrections of observables relative to the Schwarzschild black hole anywhere in space-time (outside of the horizon): the order of corrections is fixed through an eigenvalue $\mathcal{E}$ of the Einstein tensor, which is identified with an external energy momentum tensor that generates the deformation of the geometry. In this ways, $\mathcal{E}$ can be linked to effective physics models. Focusing on spherically symmetric and static black holes, I illustrate the approach at the hand of a number of observables in the vicinity of the horizon, such as characteristic quantities of particles moving around the black hole (e.g. the black hole shadow or the radius of the innermost stable circular orbit) or the spectrum of scalar quasi-normal modes. Reversing the logic, I argue that the knowledge of such observables provides non-trivial constraints on $\mathcal{E}$, which in turn grant insights into the effective physics in the vicinity of the black hole.

The static Love numbers of black holes vanish in classical, four-dimensional, asymptotically flat General Relativity. We study how this changes for the response of near-extremal Reissner--Nordström black holes to a minimally coupled massless scalar, at energies where the Schwarzian mode of the near-horizon throat fluctuates strongly. The black hole then responds as a quantum system with a spectrum of states. Its static response is a polarizability, given by virtual transitions between them. For $\ell=0$ the static Love number vanishes, by the shift symmetry of the scalar, but for multipoles $\ell\geq1$ the static Love numbers are nonzero: the finite rotational energy of the spin-$\ell$ intermediate states spoils the cancellation responsible for the classical result. Since the throat no longer has a classical geometry from which to read off a tidal response, we define it through the retarded Green's function, and compute its full frequency dependence at leading order in $r_+ω$. Its conservative part requires renormalization: the near-horizon theory fixes the coefficient of its logarithm, and with it a dependence on the energy that no local term can remove, while its finite local terms are matching data of the four-dimensional theory. The dissipative part is finite and scheme independent. For $\ell\geq1$, it vanishes at low frequencies when the energy is below the rotational gap, while at the gap threshold it becomes non-analytic in frequency and produces a late-time $t^{-3/2}$ tail.

We revisit the scenario of critical Higgs inflation, in which inflation is driven by the Standard Model Higgs boson with parameters chosen close to a critical point, giving rise to an inflection point in its potential. After reviewing this model, we perform a systematic study of its viability centered around three criteria: (1) consistency with electroweak-scale measurements, (2) ability to reproduce the cosmic microwave background (CMB) observables, and (3) sensitivity of the model predictions to unknown UV physics, based on a breakdown of perturbative unitarity. We first show that compliance with electroweak-scale measurements is controlled by the parameters in the Higgs potential at inflationary scales, also updating the literature values. We then demonstrate how for any choice of potential parameters, agreement with the CMB observables can be achieved through the choice of the nonminimal coupling, in both metric and Palatini formulations of gravity. However, we also find that there exist no regions of parameter space, in either the metric or Palatini formulations, in which compliance with all three physical criteria is possible. While this does not exclude the possibility of the Higgs field driving inflation, it means that predictions for any observable are in principle sensitive to the details of the model's UV completion.

Tidal Love numbers characterize the conservative response of compact objects to external perturbations and provide a powerful probe of their nature. While the static Love numbers of Schwarzschild, Kerr, and Reissner--Nordström black holes remarkably vanish, the tidal response of a generic Kerr--Newman black hole has remained unexplored due to the intrinsic coupling between gravitational and electromagnetic perturbations. Exploiting a recent breakthrough in the separability of these perturbations, we analytically determine the static tidal response of the most general stationary black hole in four-dimensional Einstein--Maxwell theory. For arbitrary multipole order, charge, and spin, we show that the entire matrix of conservative Love numbers vanishes, including the mixed gravito-electromagnetic couplings. We also compute the nonvanishing static dissipative response induced by frame dragging.