Thermodynamic Bethe ansatz equations for minimal surfaces in AdS 3

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. © SISSA 2010.