Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling

TL;DR

This paper explores minimal surfaces in AdS space related to eight-gluon scattering amplitudes at strong coupling, using mathematical tools like the Sinh-Gordon and Hitchin equations to obtain explicit area calculations.

Contribution

It provides an explicit computation of the minimal surface area corresponding to an eight-gluon scattering amplitude at strong coupling using integrable systems techniques.

Findings

Explicit area formula for the eight-sided null Wilson loop.

Connection between minimal surfaces and integrable equations.

Application to strong coupling scattering amplitudes.

Abstract

In this note we consider minimal surfaces in three dimensional anti-de Sitter space that end at the AdS boundary on a polygon given by a sequence of null segments. The problem can be reduced to a certain generalized Sinh-Gordon equation and to SU(2) Hitchin equations. The mathematical problem to be solved arises also in the context of the moduli space of certain three dimensional supersymmetric theories. We can use explicit results available in the literature in order to find the explicit answer for the area of a surface that ends on a eight-sided null Wilson loop. Via the gauge/gravity duality this can also be interpreted as a certain eight-gluon scattering amplitude at strong coupling for a special kinematic configuration.