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At least 1,369 records · Page 76
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DOE OSTI2026

Coarse-grained fixed-point tensor networks and holographic reflected entropy in 3D gravity

We use the framework of fixed-point BCFT tensor networks to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS 3 /CFT 2 , for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-c limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-c limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data.

AdS-CFT correspondence↗
DOE OSTI2016

Three-point functions in duality-invariant higher-derivative gravity

Here, doubled α'-geometry is the simplest higher-derivative gravitational theory with exact global duality symmetry. We use the double metric formulation of this theory to compute on-shell three-point functions to all orders in α'. A simple pattern emerges when comparing with the analogous bosonic and heterotic three-point functions. As in these theories, the amplitudes factorize. The theory has no Gauss-Bonnet term, but contains a Riemann-cubed interaction to second order in α'.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

The two-loop five-point amplitude in $\mathcal{N}$ = 8 supergravity

We compute the symbol of the two-loop five-point amplitude in $\mathcal{N}$ = 8 supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also d-dimensional ones, as the former are insufficient. Our novel d-dimensional unitarity-based approach to the systematic construction of an amplitude’s rational structures is likely to have broader applications, for example to analogous QCD calculations. We fix parameters in the ansatz by performing numerical integration-by-parts reduction of the known integrand. We find that the two-loop five-point $\mathcal{N}$ = 8 supergravity amplitude is uniformly transcendental. We then verify the soft and collinear limits of the amplitude. There is considerable similarity with the corresponding amplitude for $\mathcal{N}$ = 4 super-Yang-Mills theory: all the rational prefactors are double copies of the Yang-Mills ones and the transcendental functions overlap to a large degree. As a byproduct, we find new relations between color-ordered loop amplitudes in $\mathcal{N}$ = 4 super-Yang-Mills theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Boundary terms and three-point functions: an AdS/CFT puzzle resolved

N=8 superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators O IJ with Δ = 1 in the 35 v representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS 4 gravity dual, obtained from gauged N=8 supergravity, has no cubic A 3 couplings in its Lagrangian, where A IJ is the bulk dual of OIJ. So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS 4 boundary requires the introduction of a finite A 3 counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the Δ = 1 operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Composing effective prediction at five points

Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d 4 ) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Landau singularities of the 7-point ziggurat. Part I

We compute the leading (first-type Landau) singularities of a certain four-loop 7-point graph that is related to the 7-point “ziggurat” graph by the graphical moves familiar from equivalent circuit theory. We find perfect agreement with a subset of the “heptagon symbol alphabet” that has appeared in the context of planar Ν = 4 super-Yang-Mills theory. The remaining heptagon symbol letters are found in its subleading Landau singularities, which we address in a companion paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

The three-point energy correlator in the coplanar limit

Energy correlators are a type of observables that measure how energy is distributed across multiple detectors as a function of the angles between pairs of detectors. In this paper, we study the three-point energy correlator (EEEC) at lepton colliders in the three-particle near-to-plane (coplanar) limit. The leading-power contribution in this limit is governed by the three-jet (trijet) configuration. We introduce a new approach by projecting the EEEC onto the volume of the parallelepiped formed by the unit vectors aligned with three detected final-state particles. Analogous to the back-to-back limit of the two-point energy correlator probing the dijet configuration, the small-volume limit of the EEEC probes the trijet configuration. We derive a transverse momentum dependent (TMD) based factorization theorem that captures the soft and collinear logarithms in the coplanar limit, which enables us to achieve the next-to-next-to-next-to-leading logarithm (N 3 LL) resummation. To our knowledge, this is the first N 3 LL result for a trijet event shape. Additionally, we demonstrate that a similar factorization theorem can be applied to the fully differential EEEC in the three-particle coplanar limit, which provides a clean environment for studying different coplanar trijet shapes.

Effective Field Theories of QCD↗
DOE OSTI2021

Revisiting the multi-monopole point of SU( N ) $\mathcal{N}$ = 2 gauge theory in four dimensions

Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) $\mathcal{N}$ = 2 gauge theory in four dimensions. At this point N - 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large-N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N, finding exact agreement with our first calculation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Conformal BK equation at QCD Wilson-Fisher point

High-energy scattering in pQCD in the Regge limit is described by the evolution of Wilson lines governed by the BK equation. In the leading order, the BK equation is conformally invariant and the eigenfunctions of the linearized BFKL equation are powers. It is a common belief that at d ≠ 4 the BFKL equation is useless since unlike d = 4 case it cannot be solved by usual methods. However, we demonstrate that at critical Wilson-Fisher point of QCD the relevant part of NLO BK restores the conformal invariance so the solutions are again powers. As a check of our approach to high-energy amplitudes at the Wilson-Fisher point, we calculate the anomalous dimensions of twist-2 light-ray operators in the Regge limit j → 1.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

A 3d disordered superconformal fixed point

We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a $\mathcal{N}$= 2 large N Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large N spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.

1/N expansion↗
DOE OSTI2013

Filtering with Marked Point Process Observations via Poisson Chaos Expansion

We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fundamental Solutions for Two-Point Boundary Value Problems in Orbital Mechanics

We consider a two-point boundary value problem (TPBVP) in orbital mechanics involving a small body (e.g., a spacecraft or asteroid) and N larger bodies. The least action principle TPBVP formulation is converted into an initial value problem via the addition of an appropriate terminal cost to the action functional. The latter formulation is used to obtain a fundamental solution, which may be used to solve the TPBVP for a variety of boundary conditions within a certain class. In particular, the method of convex duality allows one to interpret the least action principle as a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. In the case where the time duration is less than a specific bound, there exists a unique critical point for the resulting differential game, which yields the fundamental solution given in terms of the solutions of associated Riccati equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Inverse point source location with the Helmholtz equation on a bounded domain

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization problems in measure space in combination with the Helmholtz equation on a bounded domain is considered in this study. A weighted norm with unbounded weight near the observation points is incorporated into the formulation. Optimality conditions and conditions for recovery in the small noise case are discussed, which motivates concrete choices of the weight. The numerical realization is based on an accelerated conditional gradient method in measure space and a finite element discretization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Critical Two-Point Function for Long-Range O(n) Models Below the Upper Critical Dimension

We consider the n-component |φ|{sup 4} lattice spin model (n≥1) and the weakly self-avoiding walk (n=0) on ℤ{sup d}, in dimensions d=1,2,3. We study long-range models based on the fractional Laplacian, with spin-spin interactions or walk step probabilities decaying with distance r as r{sup −(d+α)} with α∈(0,2). The upper critical dimension is d{sub c}=2α. For ε>0, and α=(1/2)(d+ε), the dimension d=d{sub c}−ε is below the upper critical dimension. For small ε, weak coupling, and all integers n≥0, we prove that the two-point function at the critical point decays with distance as r{sup −(d−α)}. This “sticking” of the critical exponent at its mean-field value was first predicted in the physics literature in 1972. Our proof is based on a rigorous renormalisation group method. The treatment of observables differs from that used in recent work on the nearest-neighbour 4-dimensional case, via our use of a cluster expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Boundaries of Stability Domains for Equilibrium Points of Differential Equations with Parameters

We consider autonomous and periodic differential equations containing two scalar parameters and analyze the construction of boundaries of stability domains of equilibrium points for such equations in the plane of parameters. We indicate conditions under which a unique smooth boundary curve passes through a given point. We propose a scheme of approximate construction of this curve.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Evaluation of the Index and Singular Points of Linear Differential-Algebraic Equations of Higher Order

We study linear systems of ordinary differential equations of higher order with an identically singular matrix at the higher derivative of the required vector-valued function in the domain of definition. We give definitions of the index and singular points for these systems, formulate the conditions of solvability, and deduce a formula for the general solution. The algorithms for finding the index and singular points are presented.

97 MATHEMATICS AND COMPUTING↗