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

TL;DR

This paper analyzes null-polygonal minimal surfaces in AdS_4 related to gluon scattering amplitudes, using TBA equations from perturbed W minimal models to derive analytic expansions and compare with two-loop results.

Contribution

It introduces a novel approach to solve TBA equations for minimal surfaces in AdS_4 via conformal perturbation theory, connecting to perturbed W minimal models.

Findings

Analytic expansion of the remainder function for n=6 and 7.

Close similarity between rescaled remainder and two-loop results for n=6.

Effective use of TBA systems from perturbed W minimal models in this context.

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.