arXiv subjects

Aidan Herderschee

Publications and source records attributed to Aidan Herderschee.

At least 19 recordsLinked to original sources

arXiv2026

Inner Horizon Saddles and a Spectral KSW Criterion

The Bekenstein-Hawking entropy formula $ρ= e^{A/4G}$ receives significant corrections for charged black holes near extremality. Using standard results in JT gravity, the correction term can semiclassically be expressed as minus the exponential of the inner horizon area, $e^{A_{\text{inner}}/4G}$, and the cancellation between these two exponentials enforces a vanishing density of states towards extremality, when the two horizons collide. Building on arXiv:2402.10162, we argue that the correction term corresponds to a complex saddle geometry of the bulk gravitational path integral. The proposed geometry has a negative boundary length and caps off at the inner horizon; we refer to it as the inner horizon saddle. We discuss how the saddle, and its accompanying minus sign, contribute to the density of states through a Picard-Lefschetz analysis of the inverse Laplace contour, together with a stability analysis of the saddle. We also address the inner horizon saddle's violation of the Kontsevich-Segal-Witten (KSW) allowability criterion for the inclusion of complex metrics. Despite this violation, which is believed to cause unphysical divergences in path integral computations, one can describe one-loop effects on the inner horizon saddle by carefully treating wrong-sign modes. Motivated by this observation, we propose a weaker version of the KSW criterion, which we call the spectral KSW criterion. Its purpose is to characterize when one-loop corrections around complex gravitational saddles are well defined.

hep-th↗

arXiv2026

Three Point Amplitudes in Matrix Theory

We compute the three graviton amplitude in the Banks-Fischler-Shenker-Susskind matrix model for M-theory. Even though the three point amplitude is determined by super Poincare invariance in eleven dimensional M-theory, it requires a non-trivial computation in the matrix model. We consider a configuration where all three gravitons carry non-zero longitudinal momentum. To simplify the problem, we compactify one additional dimension and relate the amplitude to a supersymmetric index computation. We find agreement with the expected answer even at finite values of $N$.

hep-th↗

arXiv2026

On the Numerical Integration of One-Loop Cosmological Collider Signals

In a broad class of inflationary models, the leading non-Gaussian bispectrum arises from one-loop rather than tree-level processes. However, realistic one-loop contributions remain largely unexplored for phenomenologically relevant masses beyond the simplest bubble diagrams. This is insufficient for observational purposes because, for generic masses and couplings, triangle contributions need not be suppressed relative to their bubble counterparts. We present a numerical method for evaluating scalar one-loop in-in diagrams contributing to the inflationary bispectrum at fully general external momenta and masses. First, the Witten-Feynman parameterization reduces de Sitter loop integrals to generalized Euler-Mellin integrals governed by Symanzik graph polynomials. Unfortunately, the exponents of the polynomials in the integrand become complex for sufficiently heavy masses, leading to sign problems when evaluating the integral using standard numerical techniques. To remedy this problem, we introduce the reduced Schwinger method, which evaluates a highly oscillatory subintegral analytically to obtain a Gauss hypergeometric kernel, leaving the remaining integrals to standard numerical quadrature. We validate the algorithm by reproducing known analytic results for the tree-level bispectrum in terms of ${}_3F_2$ functions, and then apply it to the one-loop bubble and triangle contributions at general kinematics. This yields the first direct numerical evaluation of the complete one-loop bispectrum, valid across the full kinematic range. Using these numerical results, we construct bispectrum templates and compare them with CMB data.

hep-ph↗

arXiv2026

Higher-point correlators in the BFSS matrix model

We investigate higher-point correlators in the BFSS matrix model, a non-conformal theory dual to type IIA string theory, using Witten diagrams and techniques from the amplitudes program. While the Witten diagrams are more complex than those relevant for conformal holographic theories, we find that the added complexity is minimal. As an illustration, we compute the leading three-point Witten diagram, evaluating it in a squeezed limit using the method of regions. Our results provide new targets for future Monte-Carlo and quantum simulations of the BFSS matrix model.

hep-th↗

arXiv2026

String Theory from Maximal Supersymmetry

We explore the space of non-gravitational, maximally supersymmetric, planar 4d effective field theories (EFTs) that have $\mathcal{N}=4$ super Yang-Mills (SYM) at leading order. In the weakly-coupled regime, we examine the combined constraints of $\mathcal{N}=4$ supersymmetry and $SU(4)$ R-symmetry together with the requirement of standard tree-level factorization on the massless poles of the 4-, 5-, and 6-point EFT scattering amplitudes. When imposing a parity condition on the 6-scalar amplitudes, we find highly nontrivial nonlinear constraints on the 4-point Wilson coefficients. When these novel constraints are combined with positivity, the resulting bounds on the 4-point Wilson coefficients converge to the values of the open string Veneziano amplitude. Our results strongly suggest that supersymmetry, R-symmetry, the parity requirement on the 6-scalar amplitudes, and positivity are sufficient to single out this unique UV completion at tree level. Our findings, moreover, highlight the power of higher-point amplitudes in constraining EFT data and imply that the space of consistent quantum field theories is even more restricted than previously suggested by causality or swampland-based approaches.

hep-th↗

arXiv2026

Gravitational Effective Theories with Maximal Supersymmetry and a Peculiar Parity

We study the space of four-dimensional ultraviolet completions for $\mathcal{N}=8$ supergravity that are described at low energies by weakly-coupled effective field theories (EFTs) with maximal supersymmetry and $\mathrm{SU}(4)\times\mathrm{SU}(4)$ R-symmetry. We show that tree-level factorization of the 4-, 5-, and 6-point EFT scattering amplitudes, together with a certain ``peculiar parity'' condition, leads to nonlinear constraints on the 4-point Wilson coefficients. This peculiar parity is a property that can only be imposed on a subset of scalar amplitudes. Combining the nonlinear constraints with positivity, we find that the allowed region of 4-point Wilson coefficients is reduced to a non-convex domain with two sharp corners: one being the closed superstring Virasoro--Shapiro amplitude, the other an infinite spin tower amplitude exchanging states of every spin at the same mass. We show both numerically and analytically that requiring a finite number of states near the first mass level leaves only the Virasoro--Shapiro amplitude.

hep-th↗

arXiv2026

Asymptotic Simplicity and Scattering in General Relativity from Quantum Field Theory

We investigate the fate of asymptotic simplicity in physically relevant settings of compact-object scattering. Using the stress tensor of a two-body system as a source, we compute the spacetime metric in General Relativity at finite observer distance in an asymptotic expansion. To do so, we relate the metric to the final-state graviton one-point function in momentum space, which is computed using perturbative QFT techniques. Both the simple pole and the infrared-related logarithmic branch cut in the virtuality of the external graviton contribute nontrivially. We focus on determining the fall-off behavior of the Newman-Penrose scalars, confirming previous predictions that Sachs's peeling property is violated at leading order in the post-Minkowski expansion. Our analysis at higher orders in the post-Minkowskian expansion reveals a significantly stronger breakdown of the peeling property than previously recognized, which is the result of nonlinear, long-range interactions between localized sources and the surrounding gravitational field.

hep-th↗

arXiv2025

Bounding field excursions along null geodesics with applications to cosmology

Scalar fields in theories of gravity often inhabit a moduli space of vacua, and coherent spatial or temporal variations in their expectation values can produce measurable gravitational effects. Such variations are expected in contexts ranging from inflationary cosmology to the near-horizon regions of near-extremal black holes, where they can deflect light rays and shift horizons. This work derives a quantitative field excursion bound (FEB) on scalar variations along null geodesics, expressed in terms of the expansion parameter. The bound follows from the Raychaudhuri equation, assuming that all other fields satisfy the null energy condition (NEC). It is saturated in certain spacetimes containing a timelike naked singularity. A possible generalization to semiclassical spacetimes that violate the NEC, but satisfy a strengthened version of the quantum focusing condition (QFC), is proposed. In cosmology, the FEB constrains the extent of large field excursions to be linearly bounded by the number of e-folds, independent of the inflationary model. This has notable implications for anthropic scenarios, where large excursions are often invoked to access favorable vacua.

hep-th↗

arXiv2025

Stringy algebras, stretched horizons, and quantum-connected wormholes

While the supergravity limit of AdS/CFT has been extensively explored, the regime in which stringy dynamics dominate, characterized by the emergence of an infinite tower of higher-spin massive modes, is far less understood. In this work, we leverage techniques from algebraic quantum field theory to investigate the extent to which hallmark features of bulk gravity survive at finite string tension and the emergence of intrinsically stringy phenomena. Working in the $g_s\rightarrow 0$ limit, we model excited string modes as free particles and demonstrate that the resulting Hagedorn spectrum leads to the breakdown of the split property, a strengthening of the locality principle, for regions that are within a string length of each other. We propose that this leads to a precise algebraic definition of stretched horizons and stretched quantum extremal surfaces. When stretched horizons exist, there is an associated nontrivial horizon $\star$-algebra. Furthermore, applying the algebraic ER=EPR proposal leads to the emergence of type III von Neumann factors, which provide an intriguing characterization of how such regions can have a quantum Einstein-Rosen bridge even if they are geometrically disjoint.

hep-th↗

arXiv2025

Feynman-like parameterizations of (anti-)de Sitter Witten diagrams for all masses at any loop order

Computing correlation functions in curved spacetime is central to both theoretical and experimental efforts, from precision cosmology to quantum simulations of strongly coupled systems. In anti-de Sitter (AdS) and de Sitter (dS) space, the key observables, boundary correlators in AdS and late-time correlators in dS, are obtained via Witten diagram calculations. While formally analogous to flat-space Feynman diagrams, even tree-level Witten diagrams are significantly more complicated due to the structure of bulk propagators. Existing computational approaches often focus on scalars with a specific "conformal" mass, for which propagators simplify enough to permit the use of standard flat-space techniques. This restriction, however, omits the generic internal-line masses that arise in many cosmological and holographic settings. We present the Witten-Feynman (WF) parameterization, a general representation of scalar Witten diagrams in (A)dS as generalized Euler integrals. The WF framework applies in both position and momentum space, accommodates arbitrary internal and external masses, and holds at any loop order. It directly generalizes the familiar Feynman parameterization form of Feynman integrals, making it possible to import a broad range of amplitude techniques into the curved-space setting. We illustrate the method through two applications: a generalization of Weinberg's theorem on ultraviolet convergence and a series expansion technique that can yield explicit evaluations. Our results provide a unified computational tool for (A)dS boundary correlators, opening the door to more systematic calculations relevant for upcoming experiments and simulations.

hep-th↗

arXiv2025

A Jammed Parisi Ansatz

Constraint Satisfaction Problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value $α_{\textrm{crit}}$. Above this critical value, it is exponentially unlikely that all constraints can be mutually satisfied. We calculate the probability that constraints can all be satisfied, $P(\textrm{SAT})$, for the spherical perceptron. Traditional replica methods, such as the Parisi ansatz, fall short. We find a new ansatz, the jammed Parisi ansatz, that correctly describes the behavior of the system in this regime. With the jammed Parisi ansatz, we calculate $P(\textrm{SAT})$ for the first time and match previous computations of thresholds. We anticipate that the techniques developed here will be applicable to general constraint satisfaction problems and the identification of hidden structures in data sets.

cond-mat.stat-mech↗

arXiv2025

Failure of the large-N expansion in a Bosonic Tensor Model

We study the tensor model generalization of the quantum $p$-spherical model in the large-$N$ limit. While the tensor model has the same large-$N$ expansion as the disordered quantum $p$-spherical model, its ground state is superextensive, in contradiction with large-$N$ perturbation theory. Therefore, the large-$N$ expansion of this model catastrophically fails at arbitrarily large-$N$, without any obvious signal in perturbation theory.

hep-th↗

arXiv2025

Difference Equations and Integral Families for Witten Diagrams

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as ``summation-by-parts relations'', in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

hep-th↗

arXiv2024

Gravitational Waveform: A Tale of Two Formalisms

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton's constant, $h \sim G+G^2+G^3$ (one-loop level), and correspondingly update its comparison with its classically-derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [arXiv:2312.07452 [hep-th]], the term quadratic in the amplitude in the observable-based formalism [JHEP 02, 137 (2019)] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional $(d-4)/(d-4)$ finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order $h \sim G^1$ and at order $h \sim G^3$ when including disconnected diagrams in the observable-based formalism.

hep-th↗

arXiv2023

Soft Theorems in Matrix Theory

We show that the Banks-Fischler-Shenker-Susskind matrix model for M-theory obeys the leading and subleading soft theorems expected from eleven-dimensional supergravity. The subleading soft theorem implies the amplitude is Lorentz symmetric. This is argued for general four point amplitudes, but only for restricted kinematics for five and higher point amplitudes.

hep-th↗

arXiv2023

The Sub-Leading Scattering Waveform from Amplitudes

We compute the next-to-leading order term in the scattering waveform of uncharged black holes in classical general relativity and of half-BPS black holes in $\mathcal{N}=8$ supergravity. We propose criteria, generalizing explicit calculations at next-to-leading order, for determining the terms in amplitudes that contribute to local observables. For general relativity, we construct the relevant classical integrand through generalized unitarity in two distinct ways, (1) in a heavy-particle effective theory and (2) in general relativity minimally-coupled to scalar fields. With a suitable prescription for the matter propagator in the former, we find agreement between the two methods, thus demonstrating the absence of interference of quantum and classically-singular contributions. The classical $\mathcal{N}=8$ integrand for massive scalar fields is constructed through dimensional reduction of the known five-point one-loop integrand. Our calculation exhibits novel features compared to conservative calculations and inclusive observables, such as the appearance of master integrals with intersecting matter lines and the appearance of a classical infrared divergence whose absence from classical observables requires a suitable definition of the retarded time.

hep-th↗

arXiv2023

Flattening of the EFT-Hedron: Supersymmetric Positivity Bounds and the Search for String Theory

We examine universal positivity constraints on $2 \to 2$ scattering in 4d planar $N=4$ supersymmetric Yang-Mills theory with higher-derivative corrections. We present numerical evidence that the convex region of allowed Wilson coefficients (the ``EFT-hedron'') flattens completely along about one-third of its dimensions when an increasing number of constraints on the spectral density from crossing-symmetry are included. Our analysis relies on the formulation of the positivity constraints as a linear optimization problem, which we implement using two numerical solvers, SDPB and CPLEX. Motivated by the flattening, we propose a novel partially resummed low-energy expansion of the $2 \to 2$ amplitude. As part of the analysis, we provide additional evidence in favor of the conjecture [1] that the Veneziano amplitude is the only amplitude compatible with both S-matrix bootstrap constraints and string monodromy.

hep-th↗

arXiv2023

Bootstrapping the String KLT Kernel

We show that a generalized version of the 4-point string theory KLT double-copy map is the most general solution to the minimal-rank double-copy bootstrap in effective field theory. This follows from significant restrictions of the 4-point map resulting from the 6-point bootstrap analysis. The generalized 4-point double-copy map is defined by a function with only two parameters times a simple function that is symmetric in $s,t,u$. The two parameters can be interpreted as independent choices of $α'$, one for each of the two sets of amplitudes double-copied with the map. Specifically, each of those two sets of amplitudes must obey either the string monodromy relations or the field theory KK & BCJ relations; there are no other options. We propose a closed form of the new double-copy map that interpolates between the original KLT string double-copy and the open & closed string period integrals. The construction clarifies the "single-valued projection" property of the Riemann zeta-function values for the 4-point string theory double copy.

hep-th↗