Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models

Abstract

We study the null-polygonal minimal surfaces in AdS_4, which correspond to the gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces with n cusps is characterized by the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n-4)_4/U(1)^{n-5} generalized parafermion theory perturbed by the weight-zero adjoint operators. Based on the relation to the TBA systems of the perturbed W minimal models, we solve the TBA equations by using the conformal perturbation theory, and obtain the analytic expansion of the remainder function around the UV/regular-polygonal limit for n=6 and 7. We compare the rescaled remainder function for n=6 with the two-loop one, to observe that they are close to each other similarly to the AdS_3 case.

43 pages, 8 figures; (v2) minor corrections

References in corpus (13)

• 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
• Correlation functions in conformal Toda field theory I
• Analytic Results for MHV Wilson Loops
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• Reflection factors and exact g-functions for purely elastic scattering theories
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• Scattering amplitudes at strong coupling for 4K gluons

Cited by in corpus (12)

• 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
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• ODE/IM correspondence and modified affine Toda field equations
• 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
• A short review on TBA equation and scattering amplitude/Wilson loop duality