Thermodynamic Bubble Ansatz

Abstract

Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS_5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4) Hitchin system. The polygon with six edges is the first non-trivial example. For this case, we write an integral equation which determines the area as a function of the shape of the polygon. The equations are identical to those of the Thermodynamics Bethe Ansatz. Moreover, the area is given by the free energy of this TBA system. The high temperature limit of the TBA system can be exactly solved. It leads to an explicit expression for a special class of hexagonal contours.

55 pages, 22 figures. v2: references added, V3: small typo fixed

References in corpus (15)

• Gluon scattering amplitudes at strong coupling
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• The ODE/IM Correspondence
• Comments on operators with large spin
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Generating AdS String Solutions
• Pohlmeyer reduction revisited
• On reduced models for superstrings on AdS_n x S^n
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Moduli Dynamics of AdS_3 Strings
• Eliminating spurious poles from gauge-theoretic amplitudes
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• Series Solution and Minimal Surfaces in AdS

Cited by in corpus (173)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Quantum spectral curve for AdS_5/CFT_4
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Motivic Amplitudes and Cluster Coordinates
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Y-system for Scattering Amplitudes
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Form factors at strong coupling via a Y-system
• Heptagons from the Steinmann Cluster Bootstrap
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• From correlation functions to Wilson loops
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• A Shortcut to the Q-Operator
• Wall-Crossing in Coupled 2d-4d Systems
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Webs in multiparton scattering using the replica trick
• Cluster adjacency properties of scattering amplitudes
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Harmony of Super Form Factors
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Exciting the GKP string at any coupling
• Analytic Solution of Bremsstrahlung TBA
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Cluster adjacency and the four-loop NMHV heptagon
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• TBA equations and resurgent Quantum Mechanics
• Structure constants at wrapping order
• MHV Diagrams in Momentum Twistor Space
• Quantum Sine(h)-Gordon Model and Classical Integrable Equations
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• On the collinear limit of scattering amplitudes at strong coupling
• The Double Pentaladder Integral to All Orders
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• An $S$-Matrix for Massless Particles
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• How tropical are seven- and eight-particle amplitudes?
• Analytic Results for MHV Wilson Loops
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Lifting Heptagon Symbols to Functions
• Massless scattering at special kinematics as Jacobi polynomials
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• On holographic three point functions for GKP strings from integrability
• Wave functions and correlation functions for GKP strings from integrability
• Surprises in the AdS algebraic curve constructions - Wilson loops and correlation functions
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• $R^3$ index for four-dimensional $N=2$ field theories
• All-Mass $n$-gon Integrals in $n$ Dimensions
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Wilson loop OPE, analytic continuation and multi-Regge limit
• A note on the eigenvectors of long-range spin chains and their scalar products
• Geometric aspects of the ODE/IM correspondence
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• ODE/IM correspondence for the Fateev model
• Correlation functions, null polygonal Wilson loops, and local operators
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• Wilson Loops @ 3-Loops in Special Kinematics
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• Space-like minimal surfaces in AdS x S
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• The Wilson Loop -- Large Spin OPE Dictionary
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• ODE/IM correspondence and modified affine Toda field equations
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• TBA equations for the Schrödinger equation with a regular singularity
• The Bethe Ansatz and the Tzitzéica-Bullough-Dodd equation
• Bethe Ansatz equations for the classical $A_n^{(1)}$ affine Toda field theories
• g-Functions and gluon scattering amplitudes at strong coupling
• Critical values of the Yang-Yang functional in the quantum sine-Gordon model
• Heptagon Amplitude in the Multi-Regge Regime
• The Two-Loop Remainder Function for Eight and Nine Particles
• Network, Cluster coordinates and N=2 theory I
• T-functions and multi-gluon scattering amplitudes
• The Two-Loop Symbol of all Multi-Regge Regions
• The Excited Hexagon Reloaded
• Phase transitions in Wilson loop correlator from integrability in global AdS
• Hidden Simplicity of Gauge Theory Amplitudes
• WKB periods for higher order ODE and TBA equations
• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Network, cluster coordinates and N = 2 theory II: Irregular singularity
• On the two-loop hexagon Wilson loop remainder function in N=4 SYM
• Nonperturbative enhancement of superloop at strong coupling
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• A Finite $S$-Matrix
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Towards NMHV amplitudes at strong coupling
• Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
• Wilson loop remainder function for null polygons in the limit of self-crossing
• $T$, $Q$ and periods in $SU(3)$ $\mathcal{N}=2$ SYM
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• Series Solution and Minimal Surfaces in AdS
• ABJM quantum spectral curve and Mellin transform
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Octagons II: Strong Coupling
• On the scattering of gluons in the GKP string
• Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• The four-loop six-gluon NMHV ratio function
• Hexagon remainder function in the limit of self-crossing up to three loops
• Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS_3
• On the mass-coupling relation of multi-scale quantum integrable models
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Strong Wilson polygons from the lodge of free and bound mesons
• Hitchin systems in N=2 field theory
• An Origin Story for Amplitudes
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Cluster algebras in scattering amplitudes with special 2D kinematics
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• $Y$ systems, $Q$ systems, and 4D $\mathcal{N}=2$ supersymmetric QFT
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• MHV amplitudes at strong coupling and linearized TBA equations
• A Two-Loop Four-Point Form Factor at Function Level
• Antipodal Symmetry of Two-Loop MHV Amplitudes
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Irregular Singularities in the H3+ WZW Model
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• Vacuum energy of the Bukhvostov-Lipatov model
• A Note on One-loop Cluster Adjacency in N = 4 SYM
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• From algebraic curve to minimal surface and back
• WKB analysis of the linear problem for modified affine Toda field equations
• On analytical perturbative solution of ABJM quantum spectral curve
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• ABJM flux-tube and scattering amplitudes
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• The Multi-Regge Limit from the Wilson Loop OPE
• Integrability and Wilson loops: the wavy line contour
• Spectral determinants for twist field correlators
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Locally Finite Observables in sYM
• From Fuchsian differential equations to integrable QFT
• Vacuum type space-like string surfaces in AdS_3 x S^3
• AdS String: Classical Solutions and Moduli Dynamics
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Holographic correlation functions of hexagon Wilson loops with one local operator
• Wilson loops for triangular contours with circular edges
• Spiky Strings with Two Spins in AdS5
• Multi-trace Correlators from Permutations as Moduli Space
• 12 loops and triple wrapping in ABJM theory from integrability
• $\mathcal{N}=4$ polygonal Wilson loops: fermions
• Gluon scattering amplitudes from gauge/string duality and integrability
• Hexagon Bootstrap in the Double Scaling Limit
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• Quantum TBA for refined BPS indices
• Novel aspects of integrability for NLSMs in symmetric spaces
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM