T-functions and multi-gluon scattering amplitudes

Abstract

We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling which correspond to minimal surfaces with a light-like polygonal boundary in AdS_3. We find a concise expression of the remainder function in terms of the T-function of the associated thermodynamic Bethe ansatz (TBA) system. Continuing our previous work on the analytic expansion around the CFT/regular-polygonal limit, we derive a formula of the leading-order expansion for the general 2n-point remainder function. The T-system allows us to encode its momentum dependence in only one function of the TBA mass parameters, which is obtained by conformal perturbation theory. We compute its explicit form in the single mass cases. We also find that the rescaled remainder functions at strong coupling and at two loops are close to each other, and their ratio at the leading order approaches a constant near 0.9 for large n.

36 pages, 5 figures, v2: published version, v3: minor corrections

References in corpus (14)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Form factors at strong coupling via a Y-system
• Bootstrapping Null Polygon Wilson Loops
• Analytic Results for MHV Wilson Loops
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Reflection factors and exact g-functions for purely elastic scattering theories
• g-Functions and gluon scattering amplitudes at strong coupling
• Scattering amplitudes at strong coupling for 4K gluons

Cited by in corpus (13)

• Hexagon functions and the three-loop remainder function
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• ODE/IM correspondence and modified affine Toda field equations
• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• Exact mass-coupling relation for the homogeneous sine-Gordon model
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• On the mass-coupling relation of multi-scale quantum integrable models
• MHV amplitudes at strong coupling and linearized TBA equations
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• Gluon scattering amplitudes from gauge/string duality and integrability