TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling

TL;DR

This paper develops an analytic method using TBA-like equations to compute the non-planar correction to gluon scattering amplitudes at strong coupling in N=4 SYM, linking minimal surfaces in AdS to integrable systems.

Contribution

It introduces a novel approach connecting Hitchin systems and TBA equations to analytically compute minimal areas related to non-planar amplitudes.

Findings

Analytic expressions for minimal areas using TBA-like equations.

Agreement between TBA-based calculations and numerical integration.

Extension of AdS/CFT techniques to non-planar corrections at strong coupling.

Abstract

We compute the minimal area of a string worldsheet ending on two infinite periodic light-like Wilson lines in the AdS$_3$ boundary, which is dual to the first non-planar correction to the gluon scattering amplitude in $\mathcal{N}=4$ SYM at the strong coupling. Using the connection between the Hitchin system and the thermodynamic Bethe ansatz (TBA) equations, we present an analytic method to compute the minimal area surface and express the non-trivial part of the minimal area in terms of the free energy of the TBA-like equations. Given the cross ratios as inputs, the area computed from the TBA-like equations matches that calculated using the numerical integration.