Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3

TL;DR

This paper derives thermodynamic Bethe ansatz equations for minimal surfaces in AdS_3, linking classical string solutions with gluon scattering amplitudes and identifying connections to sine-Gordon models and parafermions.

Contribution

It provides a detailed derivation of integral equations for specific polygonal solutions in AdS_3 and relates them to known integrable models, advancing understanding of AdS/CFT correspondence.

Findings

Derived TBA equations for decagonal and dodecagonal solutions

Connected minimal surfaces in AdS_3 to sine-Gordon models

Computed central charges indicating correspondence with parafermions

Abstract

We study classical open string solutions with a null polygonal boundary in AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS_n and generalized parafermions.