Papers

Gravitational waves couple in a nonlinear fashion in the vicinity of a black hole. Black hole perturbation theory can be readily applied to compute the magnitude of this coupling, its dependence on the parity content, frequencies, and angular structure of the incoming gravitational waves. In this work we carry out this calculation, showing how the nonlinear coupling of gravitational waves generically peaks when the driven frequency matches the oscillation frequency of the fundamental quasinormal mode of the black hole. We also demonstrate how this excitation is largest at the maximal harmonics allowed, and study its dependence on the parity content of the incoming modes. At low frequencies, the quadratic response computed here encodes the nonlinear, dynamical tidal deformability of the black hole spacetime itself. We demonstrate numerically that the quadratic black hole coupling coefficient scales quadratically with the driving frequency, and recover this scaling from the 5-point Compton graviton scattering amplitude.

We introduce a bootstrap method for deriving bounds on disorder-averaged observables in classical statistical systems with quenched disorder. The three main ingredients of the bootstrap are the positivity of ensembles of probability measures, disorder-averaged equations of motion, and explicit expectation values of random coupling variables. Together, these ingredients lead to a linear programming problem over the space of disorder averages. By further employing the positivity of the two-replica Gram matrix, we also formulate a semidefinite programming problem that produces bounds on two-replica correlators. We demonstrate the method using two examples: the two-dimensional random site-diluted Ising model and the one-dimensional disordered contact process. For the latter example, the bootstrap bounds exhibit a region of multiple kinks that we relate to the Griffiths region, whose finite-size scaling analysis yields a typical correlation length exponent in good numerical agreement with the known value.

Integrating out heavy particles is generally viewed as an irreversible procedure that erases some physical information above the cutoff scale of the resulting effective theory. However, this does not preclude the possibility of recovering the heavy propagating degrees from the low-energy effective theory with appropriate boundary data supplied. A classic example is the recovery of Schwinger pair production from the resummed Euler-Heisenberg effective action. In this work, we perform a similar exercise in a cosmological setting. We show that it is possible to reconstruct the inflationary correlators with massive exchanges, for a discrete heavy spectrum and arbitrary tree topologies, from the low-energy effective theory together with unitarity and Bunch-Davies boundary conditions. The divergent EFT series is resummed in three ways: the boundary differential operators, spectral representation, and Borel resummation, and the exponentially suppressed cosmological collider signals are recovered via analytic continuation. Our construction provides a resurgent relation between the local EFT background and the nonanalytic heavy-particle production, and may also be viewed as an inverse problem for the dispersive bootstrap.

We provide a simple derivation of the conformal dispersion relation of Carmi and Caron-Huot which reconstructs a CFT four-point function from its double discontinuity. We exhibit a hidden conformal symmetry which explains the appearance of the "magic variable" x as a simple cross-ratio, built from four physical cross-ratios. We also introduce a regulator in the double discontinuity operation and then prove that one subtraction suffices for all integrals to converge.

We propose an M-theory origin for the two massive deformations of type 0A string theory by extending Hull's realization of massive type IIA in the context of a recent proposal for massless type 0A from M-theory. We introduce an M-theory setup that we call quantum fibration, in which two independent integral monodromies yield the Romans masses, T-dual to the two Chern numbers of the quantum fibration. A key ingredient is a formulation of the type 0B duality group in terms of a marked elliptic curve. We discuss further implications of this description and some puzzles concerning the M-theory origin of branes and Chern–Simons terms.

We study the gauging of discrete symmetries of the 5d rank-one $E_n$ SCFTs that fix the Coulomb branch coordinate but act nontrivially on the Higgs branch chiral ring. Using generalized toric polygons and $(p,q)$-brane webs, we identify symmetries of the moduli space that extend to symmetries of the full SCFT. In many cases they are non-anomalous, and we analyze the moduli space of the gauged theories. We realize the resulting Higgs branch quotients as Coulomb branches of wreathed magnetic quivers and compute their Hilbert series; the flavor algebras extracted from moment maps agree with the fixed-point subalgebras of $\mathfrak{e}_n$. We also lift the discrete actions to the Seiberg–Witten geometry and recover the expected restriction on the mass deformations. For $\mathbb{Z}_2$-wreathings that exchange adjacent gauge nodes, we find that the monopole formula requires a flux-dependent sign and propose a corrected prescription. Finally, we conjecture a higher-rank extension and verify it for the rank-two $E_6/\mathbb{Z}_2$ Higgs branch.

We present evidence that ten-dimensional type IIB string theory orbifolded by the $\mathbb{Z}_3$ duality symmetry at the strong-coupling fixed point $\tau=\exp(2\pi i/3)$ 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 $\Gamma^{2,2}(A_2)$ ($S_3 \times S_3 \times \mathbb{Z}_2$). 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.

Using on-shell methods, we derive an all-order non-renormalization theorem for general four-dimensional effective field theories, relying on Poincaré invariance and unitarity. Each operator $\mathcal O$ is assigned the weights $(w,\bar w)=(\ell-h,\ell+h)$, where $\ell$ and $h$ are the number of particles and total helicity of its minimal configuration. At $L$ loops, the mixing $\mathcal O_j\to\mathcal O_i$ vanishes when $\ell_j-\ell_i=L-1$ and either $w_i<w_j-2(L-1)$ or $\bar w_i<\bar w_j-2(L-1)$, in the absence of non-holomorphic Yukawa couplings. These zeros follow entirely from tree-level data and are scheme independent under finite renormalizations that preserve the operator-length selection rule. For operators of dimensions five through eight, we identify broad classes of previously unknown zeros at higher loop orders, with particular emphasis on two loops, where the theorem provides direct checks on current calculations, as in the Standard Model Effective Field Theory.

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 $\mathcal{L} \supset c_\psi\,\frac{\partial_\mu a}{f_a}\, \psi^\dagger \bar{\sigma}^\mu \psi$ with $c_\psi$ 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 $\alpha_{\rm YM}$ 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.

Anomalies of generalized symmetries are closely related to the statistics of topological excitations. Truncating a symmetry transformation to a finite region produces an operator that creates symmetry defects on its boundary; we call this a symmetry patch operator. Such operators resemble hopping operators that create topological excitations at the boundary of their support, but this geometric similarity does not justify identifying the two. For finite Abelian groups in one spatial dimension, we prove that if the same family of local operators defines both valid hopping operators and compatible symmetry patches, the type-III component of the anomaly is $-2$ times that of the statistics. We establish a one-to-one correspondence between statistics and anomaly by treating hopping operators as symmetric operators that commute with the global symmetry, following the description of symmetry through the algebra of local symmetric operators. We explain this correspondence through gauging by coupling boundary matter to a Dijkgraaf-Witten gauge field in one higher spatial dimension. Hopping operators act on the gauge-invariant degrees of freedom. After fixing the background gauge field, the residual gauge transformations become the global symmetry, and the gauge invariance of hopping operators becomes the requirement that they commute with this symmetry.

We study a new class of M2-brane matrix models associated with affine BC and twisted affine AD quivers. These models exhibit the characteristic $N^{3/2}$ scaling of the free energy in the large $N$ limit. We establish a Fermi gas formalism and demonstrate that their grand canonical sum is given by a Fredholm Pfaffian, which is in parallel with the affine D quiver matrix models. The resulting Fermi gas density matrix shows a rational dependence on the canonical position/momentum operators in addition to the standard hyperbolic dependence. This leads to unconventional sub-leading corrections, which obstruct the Airy function structure in the $1/N$ expansion of the free energy observed in the previously studied M2-brane matrix models.

Quantum effects are expected to modify a black hole's interior structure, particularly near the singularity. We show how to extract the scaling exponent of the singularity from the quasinormal mode (QNM) spectrum of a massless scalar probe in the asymptotic large-overtone limit. We apply our method to a family of exact quantum black holes in (2+1)-dimensional anti-de Sitter (AdS) space and explicitly uncover a transition deep in the interior when quantum effects become dominant.

We develop a hydrodynamic effective field theory for the gravitational dynamics of compact objects moving through an inviscid fluid environment. The fluid is described by the effective theory of perfect fluids, whose Goldstone phonons are kept as explicit fields coupled to gravity. We establish a consistent power counting for the resulting Feynman rules and derive the propagators and interaction vertices through four points in $D$ dimensions, together with the generalized on-shell Ward identities they obey. These identities relate amplitudes with an external graviton to those with the graviton replaced by a phonon, and thus provide nontrivial checks on higher-order calculations. As an application, we recover the leading-order relativistic dynamical-friction force from the tree-level amplitude for single-phonon emission. This work is a first step towards a toolkit for incorporating environmental effects into the scattering-amplitude pipeline used in post-Minkowskian calculations.

We investigate the electromagnetic form factors of the $\rho$ meson family within a holographic QCD framework based on Einstein-dilaton gravity with confining backgrounds. We obtain the elastic and transition form factors using a spectral decomposition of the three-point isospin current correlator and an independent approach based on the Kaluza-Klein expansion. Furthermore, we establish a holographic dictionary of the current matrix element. The elastic form factors are in agreement with available lattice QCD results, whereas the transition form factors, not yet determined within lattice QCD, are predictions of the model. For the elastic case, the electric form factor for the $\rho$ meson family exhibits a zero at $q^{2} = 6\, m_{\rho^{n}}^{2}$ and in particular for the ground state $q^{2} = 3.61\,\text{GeV}^{2}$, consistent with light-front and Dyson-Schwinger calculations. We also compute strong couplings between vector meson states and find some approximate selection rules. In the elastic case and low-$q^{2}$ regime, we calculate dimensionless electric radius, magnetic and quadrupole moments and compare with other approaches. In the high-$q^{2}$ regime, the form factors follow the expected scaling behavior, and the model predicts their asymptotic normalization. The results in the high-$q^{2}$ regime lead to superconvergence relations and establish a new sum rule involving masses, decay constants and couplings.

In recent work, McNamara and Wang demonstrated that the failure of factorization for a gravitational path integral (GPI) can be understood as an incompleteness of its spectrum of states by constructing a unitary quantum field theory (QFT) into which the GPI embeds. We examine this construction from an algebraic point of view, and use it to verify a conjecture of the author concerning the existence and uniqueness of a unitary completion for the GPI by means of the theory of conditional expectations. We explore how the unitary QFT can be regarded as a single coherent theory in which the quantitative signatures of ensemble averaging emerge purely from projecting to the underlying, smooth GPI. The conditional expectation relating the two theories may therefore be interpreted as a filter in the sense of Liu. The factorizing theory differs from a more standard QFT in the sense that it is reducible, meaning the Hilbert space associated with the empty set is non-trivial. We explain how the structure of reducible QFTs are generically encoded in weak Hopf algebraic symmetries and demonstrate how the weak structure allows for generalized $\alpha$-sectors and half wormholes to coexist within a single Hilbert space.

On the occasion of Gerard 't Hooft's 80th birthday, I present my personal recollections of a scientific meeting held in the Orsay Campus of the University of Paris in January 1972. In this meeting Gerard gave for the first time a detailed account of his groundbreaking work on the renormalization properties of Yang-Mills theories, both in the massless phase as well as in the phase with spontaneous symmetry breaking.

The use of nonperturbative Wilsonian functional renormalization group (FRG) equations within an unavoidable approximation scheme produces physical results that depend on the choice of the coarse-graining regulator. This dependence of physical observables on the regulator can be minimized according to the principle of minimal sensitivity (PMS). For the 1PI formulation based on the Wetterich-Morris equation, we propose to investigate the optimal choice within a space of compactly supported polynomial regulators parametrized by a set of variables. We test this approach using the derivative expansion of the effective average action up to fourth order, applying it to the scalar field theory representing the three-dimensional Ising universality class and minimizing the dependence of the anomalous dimension on the regulator. At fourth order, we find appreciable corrections to the critical exponents that improve the predictions, compared to previous one parameter analyses. We also observe families of compact regulators that rapidly converge towards an optimal functional form as a small number of parameters is progressively introduced.

We present a real time formalism to numerically describe the gravitational collapse of a scalar quantum field in the spherically symmetric case. We employ a Pauli-Villars regulator that is specifically designed to cancel the ultraviolet divergences in the energy-momentum tensor identified by covariant point splitting, including the logarithmic ones. Using this regulator, we find that the leading term of the entanglement entropy, which is proportional to the surface area, vanishes for a spherical region of flat spacetime. First numerical results for the dynamical case indicate that for a collapsing shell of a massless scalar field, the area normalized entropy is concentrated on the shell and has an approximately constant maximum value during time evolution. This maximum value appears to be finite in the continuum limit and only mildly dependent on the regulator mass.

We study the superconformal index of four-dimensional $\mathcal{N}=2$ $\mathrm{SU}(N)$ elliptic models through the Bethe Ansatz approach, where the index is evaluated as a sum of vacua arising from a set of transcendental equations. Starting from the known discrete solutions of these equations, that we refer to as progenitors, we show that there exist large classes of new descendant solutions. We then show that the solutions can be organized into orbits of the S-duality group, mimicking its action on the massive vacua of the $\mathcal{N}=1^*$ deformations of the elliptic spin Calogero-Moser models. In this way we generalize the results already obtained for $\mathcal{N}=4$ $\mathrm{SU}(N)$ SYM, where a relation between the discrete solutions to the Bethe Ansatz Equations and the massive vacua of its $\mathcal{N}=1^*$ massive deformation was conjectured. We conclude our analysis by determining the contributions of the new descendant solutions to the index.

We introduce new coordinates that extend the Kerr–Newman–Bertotti–Robinson spacetime consistently with the previous reciprocal continuation. In these coordinates, the two points at $\Omega=0$ are resolved into complete Bertotti–Robinson null infinities. The extended spacetime describes two black holes sharing a common exterior of nontrivial topology, together with a naked ring singularity. In the regular static limit, the new coordinates globally identify the spacetime with the balanced Alekseev–García geometry.

In this paper we propose a geometrically motivated formulation of gravity in an invariant Weyl–Integrable space-time (IWIST), in which the background geometry is not imposed a priori but is dynamically determined through the Palatini variational principle. For a scalar field non-minimally coupled to gravity action, the resulting compatibility condition defines a Weyl–Integrable geometry which is preserved by a local Weyl transformation of the metric and the geo\-me\-tri\-cal scalar field. We construct an action invariant under both diffeomorphisms and Weyl transformations and introduce a Weyl-covariant variational procedure based on an invariant extension of the divergence theorem. The corresponding field equations are obtained for the metric, the Weyl scalar, and the Weyl gauge field. We further formulate the theory in the Einstein–Riemann frame, where the effective metric is Riemannian and the scalar field is re\-inter\-pre\-ted as a phy\-si\-cal degree of freedom of geometric origin. Finally, we propose a geometrical mechanism for the explicit breaking of Weyl symmetry by introducing a coupling between the Weyl gauge field and a current constructed from the scalar sector. The resulting theory remains diffeomorphism covariant while departing from local Weyl invariance. The Einstein–Riemann representation of the broken theory contains an additional generally covariant interaction, making the Weyl-invariant model a particular limit of a more general gravitational theory.

A verified Kubo-Martin-Schwinger (KMS) relation, after a drive has ceased, is not sufficient evidence to prove equilibrium. We demonstrate this in a large-$N$ large-$q$ Sachdev-Ye-Kitaev (SYK) quench protocol. Although all post-quench fermion correlators are exactly thermal, a second quench back to the initial Hamiltonian reveals hidden memory of the initial state. It is encoded in correlators connecting to times before the first quench. This memory is an extensive nonequilibrium (NEQ) witness with its decay rate being the Lyapunov exponent $\lambda_L$. Thus $\lambda_L$ sets the rate at which the state becomes effectively indistinguishable from a Gibbs state. Despite being a unitary interacting many-body system, the complete NEQ real-time evolution is obtained exactly in the large-$N$, large-$q$ limit, making the setup ideal for analytically studying thermalization.

The study of phase transitions plays an important role in understanding qualitative changes in the behaviour of physical systems at criticality. Despite decades of progress, there is still a strong demand for high-precision numerical tools capable of resolving subtle critical phenomena. Motivated by this need, in this thesis, we present two complementary numerical investigations of phase transitions in lattice systems. The first uses GPU-accelerated higher-order tensor renormalization group (HOTRG) techniques to study the two-dimensional generalized XY model, characterizing its ferromagnetic, nematic, and paramagnetic phases and mapping their phase boundaries using thermodynamic observables in the thermodynamic limit. The second develops and benchmarks a configurational temperature estimator, constructed from gradients and Hessians of the Euclidean lattice action, in compact U(1) lattice gauge theories. On one hand, tensor network methods capture rich phase structures when truncation and finite-bond effects are adequately controlled. On the other hand, the configurational temperature estimator provides an independent, low-overhead means of validating thermal sampling across different algorithms and models, and can also be used as a runtime diagnostic to identify sampling pathologies before large-scale production runs.

We consider heavy-heavy-light-light (HHLL) holographic correlators in which the heavy states are coherent superpositions of $n$-particle operators. In the limit of large $n$ and large central charge, $c$, with $n/c$ held fixed, these HHLL correlators are described by a classical supergravity computation. When the multi-particle operators are half-BPS, it has been shown that the $n/c\to 0$ limit of the HHLL correlator encodes the tree-level connected contribution to the 4-point function with the heavy operators replaced by two $n$-particle operators with finite $n$. We provide evidence that this relation continues to hold when the multi-particle operators are non-supersymmetric. Although our checks are carried out in the AdS$_3$/CFT$_2$ setting, we expect that our conjecture extends to more general holographic dualities.

We review Raju's all-line recursion relations for Yang-Mills theory in AdS${}_4$ and evaluate four-point correlators for the All-plus, Single-minus, and MHV helicity configurations. We point out the relevant deformation for the legs needed to obtain the correlators. In particular, we explicitly derive the expressions for all the residues contributing to all three correlators. We also perform an explicit numerical check with the results computed by Witten diagram computations and find perfect agreement with our results. Finally, we conclude by discussing some applications of these recursions for obtaining higher-point functions.

The Page curve and the island formula describe a reorganization of quantum information in Hawking radiation across the Page time. We study how this reorganization appears in correlations among emissions collected at several retarded times. The late radiation is treated as a covariant multi-time process, or process tensor, and $\chi_{\mathrm{island}}=\mathcal{N}_{\varnothing}-\mathcal{N}_{R}$ measures the temporal memory removed when the early radiation register $R$ is supplied. Operationally, this quantity is the corresponding change in the optimal distinguishability of the radiation process from a Markovian reference. We exhibit evaporation processes whose single-bin states and all process marginals below a finite order $k_\ast\geq 3$ remain fixed and coincide with a CP-divisible reference, while $\chi_{\mathrm{island}}$ changes by order one at order $k_\ast$. The Page transition can therefore appear as a transition in the Markov order of the radiation process. When the interior mediates the late-time memory, entanglement-wedge reconstruction of the predictive interior from $R$ Markovianizes the late process; conversely, when the late process has a minimal predictive memory and its future-affecting information is mediated by that memory, Markovianization by $R$ supplies a simulator of its influence. A Hayden–Preskill evaporation comb and an evaporating-JT calculation realize this mechanism. The late radiation retains temporal memory across the transition, while the early radiation becomes sufficient for predicting its future multi-time statistics.

We study supersymmetric boundary dynamics in AdS$_3$ gravity by treating boundary conditions as constrained reductions of a generic Chern-Simons boundary phase space. We focus on how the constraint structure controls the locality and physical field content of the reduced asymptotic symmetry algebra. For supersymmetric Kac–Moody boundary conditions, the surviving bosonic currents remain local, whereas the fermion–fermion Dirac bracket contains the inverse of a field-dependent first-order differential operator and is therefore intrinsically non-local. Imposing an additional fermionic constraint reveals a further structure: after the bosonic second-class reduction, it becomes first class and generates a fermionic gauge redundancy. Generically the remaining fermionic field can be gauged away, while special backgrounds with periodic zero modes support non-trivial physical fermionic sectors. We further employ the Batalin–Fradkin–Tyutin formalism to eliminate the non-locality of the reduced symmetry algebra by converting the second-class constraints into an equivalent local first-class system on an enlarged phase space.

Kramers-Wannier duality of the quantum Ising chain is naturally realized as a noninvertible transformation on a finite periodic chain. Upon incorporating appropriate symmetry-twisted sectors, however, the duality can be promoted to an invertible unitary transformation. In this Letter, we classify when the Kramers-Wannier duality admits an invertible realization on a finite Hilbert space. We show that this is determined by the representation of the Ising bond algebra and establish a necessary and sufficient condition in terms of its two central elements. This representation-theoretic criterion unifies the conventional noninvertible realization with invertible constructions involving symmetry-twisted sectors and applies equally to other models with the same underlying bond algebra. As an explicit example, we find an order-disorder duality in a non-trivial realization of the Ising bond algebra that admits an invertible Kramers-Wannier duality.

Using the exact renormalization group (functional RG) formalism, we construct the energy-momentum tensor of a four-Fermi theory in the Euclidean space of dimensions 2 < D < 4 in the large N limit, where N is the number of Dirac fields. The energy-momentum tensor is a functional of the Dirac fields, and its cutoff dependence is controlled by the exact RG equation. In the zero cutoff limit the functional reduces to the one-particle-irreducible effective action with a single insertion of the energy-momentum tensor. At a finite cutoff the energy-momentum tensor satisfies the Ward-Takahashi identity for translation invariance, and its antisymmetric part is determined by rotation invariance. We also show that the critical theory is conformally invariant by deriving the corresponding Ward-Takahashi identity.

The Chiral anomaly cancellation is perturbatively well understood but its nonperturbative validity in presence of a lattice has remained unproven. We provide a rigorous nonperturbative proof of anomaly cancellation and its universality in a variation of the lattice Kogut-Susskind regularization for the multiflavor Sommerfield model, describing Dirac fermions interacting with a non-compact $\mathrm{U}(1)$ quantum vector field. We identify a novel and general mechanism based on the convergence properties of the renormalized expansion and related to the one leading to universality in topological insulators. Irrelevant lattice operators, despite being suppressed along the RG flow, provide essential contributions to the anomaly cancellation.