String hypothesis for the AdS_5 x S^5 mirror

TL;DR

This work identifies the states that contribute in the thermodynamic limit of the AdS5xS5 mirror theory obtained by a double-Wick rotation, by deriving the mirror Bethe-Yang equations and formulating a string hypothesis. It shows that auxiliary roots organize into Hubbard-model–like string configurations, enabling a complete description of bound states and their string centers through a nested Bethe ansatz. By relating the auxiliary equations to Lieb-Wu equations, the authors establish a Hubbard-mapping viewpoint that clarifies the structure of the thermodynamic spectrum and the regular solutions corresponding to highest-weight states. The framework lays the groundwork for a subsequent thermodynamic Bethe Ansatz treatment of the mirror model and the computation of finite-volume spectra, with explicit parametrizations of the mirror dispersion and the $u$-rapidity variables.

Abstract

We discuss the states which contribute in the thermodynamic limit of the mirror theory, the latter is obtained from the light-cone gauge-fixed string theory in the AdS_5 x S^5 background by the double-Wick rotation. We analyze the Bethe-Yang equations for the mirror theory and formulate the string hypothesis. We show that in the thermodynamic limit solutions of the Bethe-Yang equations arrange themselves into Bethe string configurations similar to the ones appearing in the Hubbard model. We also derive a set of equations describing the bound states and the Bethe string configurations of the mirror theory.