Thermodynamic Bubble Ansatz

TL;DR

This paper links the computation of minimal surfaces in AdS_5 with null polygon boundaries to a thermodynamic Bethe ansatz system, providing exact solutions for certain geometric configurations relevant to scattering amplitudes.

Contribution

It introduces a novel mapping of minimal surface problems to an SU(4) Hitchin system and derives an integral equation connecting the surface area to a TBA system, including explicit solutions in special cases.

Findings

Derived an integral equation for the polygonal surface area.

Connected the surface area to the free energy of a TBA system.

Obtained explicit solutions for hexagonal contours in the high temperature limit.

Abstract

Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS_5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4) Hitchin system. The polygon with six edges is the first non-trivial example. For this case, we write an integral equation which determines the area as a function of the shape of the polygon. The equations are identical to those of the Thermodynamics Bethe Ansatz. Moreover, the area is given by the free energy of this TBA system. The high temperature limit of the TBA system can be exactly solved. It leads to an explicit expression for a special class of hexagonal contours.