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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Bootstrap Principle for the Spectrum and Scattering of Strings

We show that the Veneziano amplitude of string theory is the unique solution to an analytically solvable bootstrap problem. Uniqueness follows from two assumptions: faster than power-law falloff in high-energy scattering and the existence of some infinite sequence in momentum transfer at which higher-spin exchanges cancel. The string amplitude—including the mass spectrum—is an output of this bootstrap. If the amplitude merely vanishes at high energies, the solution is a three-parameter family containing the Veneziano, Coon, and hypergeometric amplitudes, and more.

Field & string theory models & techniques↗
DOE OSTI2024

Nonlinear Sigma model amplitudes to all loop orders are contained in the Tr ( Φ 3 ) theory

Scattering amplitudes for the simplest theory of colored scalar particles—the Tr ( Φ 3 ) theory—have recently been the subject of active investigations. In this work we describe an unanticipated wider implication of this work: the Tr ( Φ 3 ) theory secretly contains nonlinear sigma model (NLSM) amplitudes to all loop orders. The NLSM amplitudes are obtained from Tr ( Φ 3 ) amplitudes by a unique shift of kinematic variables. We show that this shifted kinematics produces amplitudes for a cubic theory with a linear term in the potential, with extrema spontaneously breaking U ( N ) → U ( N − k ) × U ( k ) . The Goldstone amplitudes for this theory coincide with those of pions in the U ( N ) × U ( N ) → U ( N ) chiral Lagrangian to all orders in the planar limit. We also give a purely on-shell understanding of this correspondence, showing that integrands defined by the kinematic shifts have the correct residues on poles and appropriately produce the Adler zero. Finally, we discuss how similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr ( Φ 3 ) scalars, most of which are not interpretable from the Lagrangian description. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Machine learning BPS spectra and the gap conjecture

We explore statistical properties of Bogomol’nyi-Prasad-Sommerfield q-series for strongly coupled supersymmetric theories that correspond to a particular family of three-manifolds. We discover that gaps between exponents in the -series are statistically more significant at the beginning of the -series compared to gaps that appear in higher powers of. Our observations are obtained by calculating saliencies of -series features used as input data for principal component analysis, which is a standard example of an explainable machine learning technique that allows for a direct calculation and a better analysis of feature saliencies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

On the holographic dual of a symmetry operator at finite temperature

Topological symmetry operators of holographic large 𝑁 CFT 𝐷 ’s are dual to dynamical branes in the gravity dual AdS 𝐷+1 . We use this correspondence to establish a dictionary between thermal expectation values of symmetry operators in the Euclidean CFT 𝐷 and the evaluation of gravitational saddles in the presence of a dynamical brane. Expectation values of 0-form symmetry operators in the CFT 𝐷 are then related to branes wrapped on volume minimizing cycles in the bulk, i.e., the Euclidean continuation of a black hole horizon. We illustrate with some representative examples, including gravity in AdS 3 , duality/triality defects in four-dimensional 𝒩 = 4 super Yang-Mills theory, and the dual of R-symmetry operators probing five-dimensional Bogomol’nyi–Prasad–Sommerfield black holes.

Anomalies↗
DOE OSTI2024

Unitarity of bespoke amplitudes

We use partial wave unitarity to constrain various bespoke four-point amplitudes. We start by constructing bespoke generalizations of the type-I superstring amplitude, which we show satisfy dual resonance and have suitable high-energy limits. By analyzing the behavior of partial wave coefficients for highly massive states, we strictly rule out all bespoke amplitudes with asymptotically nonlinear Regge trajectories and place constraints on the first few nontrivial parameters in asymptotically linear cases. Finally, we argue that while a large class of unitary bespoke amplitudes fails to satisfy Regge sum rules, there exists a smaller subclass with a vanishing mass gap that is superpolynomially bounded.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

String-based parametrization of nucleon GPDs at any skewness: A comparison to lattice QCD

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) valid at all skewness values. The conformal moments of the GPDs are expressed as sums of the spin-j nucleon A-form factor and the skewness-dependent spin-j nucleon D-form factor. This representation, which fulfills the polynomiality condition (due to Lorentz invariance) and does not rely on model-specific assumptions, is derived from t-channel string exchanges in anti-de Sitter spaces. The spin-j nucleon D-form factor is closely related to the spin-j nucleon A-form factor. We use the Mellin moments from empirical parton distributions to model the spin-j nucleon A-form factors. Using only five Regge slope parameters, fixed from the electromagnetic and gravitational form factors, our string-based parametrization generates accurate singlet, nonsinglet, isovector, and flavor-separated nucleon quark GPDs, along with symmetric nucleon gluon GPDs from their Mellin-Barnes integral representations. Our isovector nucleon quark GPD is in agreement with existing lattice data. Our string-based parametrization should facilitate the empirical extraction and global analysis of nucleon GPDs in exclusive processes, bypassing the deconvolution challenge.

Electron-ion collisions↗
DOE OSTI2025

Uniqueness criteria for the Virasoro-Shapiro amplitude

The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from the assumptions of faster than power-law falloff at high energies and a property dubbed level truncation. At present there is no analogous principle for closed string scattering, which is famously rigid and naively impervious to modification. In this paper we analytically bootstrap the spectrum and four-point amplitudes of the closed string—together with a parametrized space of deformations—from conditions on high-energy falloff and level truncation. While these deformations exhibit the same Regge scaling as pure gravity, in the tensionless limit they reproduce remarkable extremal amplitudes that have appeared in bottom-up studies of positivity.

Field & string theory models & techniques↗
DOE OSTI2025

Antipodal self-duality of square fishnet graphs

In strongly deformed planar 𝒩 = 4 super-Yang-Mills theory, or fishnet theory, a point-split single-trace correlation function of four dimension-𝑚 scalar operators is given by a single Feynman integral, which involves integrating over locations of a 𝑚 × 𝑚 grid of points. We show that for any integer 𝑚 this square fishnet graph is invariant under the combined action of a kinematic map and the antipode map of the Hopf algebra on multiple polylogarithms; i.e. it possesses an antipodal self-duality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Multipositivity bounds for scattering amplitudes

Lorentz invariance, unitarity, and causality enforce powerful constraints on the theory space of physical scattering amplitudes. However, virtually all efforts in this direction have centered on the very simplest case of four-point scattering. In this work, we derive an infinite web of “multipositivity bounds” that nonlinearly constrain all tree-level higher-point scattering amplitudes under similarly minimal assumptions. Our construction rules out several deformations of the string and implies mixed-multiplicity bounds on the Wilson coefficients of planar effective field theories. Curiously, an infinite class of multipositivity bounds is exactly saturated by the amplitudes of the open string.

effective field theory↗
DOE OSTI2025

Holography: Quantum Mechanical Aspects of Black Holes (Final Report)

Current theories of fundamental physics are based on quantum field theory, unifying quantum mechanics and special relativity. A similar unification of quantum field theory with gravity has been elusive. String theory is a consistent model of quantum gravity and it is important to identify general lessons that can be applied to the real world. The main technique that emerged from such studies has been the gravitational path integral. During the period of this grant, the PI has explored the implication of the gravitational path integral in novel setups to uncover new features of rotating black holes in four dimensions, as well as increasing our understanding of some specific black holes in string theory.

79 ASTRONOMY AND ASTROPHYSICS↗