Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
Diego Bombardelli, Davide Fioravanti, Roberto Tateo
TL;DR
This paper constructs a nonperturbative thermodynamic Bethe Ansatz framework for planar AdS5/CFT4 by starting from the mirror theory and performing a Takahashi-like string analysis to obtain a complete set of root-density equations. It then derives the TBA equations for the pseudoenergies and demonstrates a universal Y-system structure, showing strong parallels with the Hubbard model and aligning with a Y-system recently proposed for AdS/CFT by Gromov, Kazakov, and Vieira. The work emphasizes a Hubbard-model-like organization of excitations and discusses how excited-state information may be accessed via NLIE methods, while also touching on fugacity-based refinements related to a Witten-index-like quantity. Overall, it provides a cohesive, nonperturbative path toward understanding the AdS/CFT spectrum across coupling regimes through a Y-system framework grounded in the mirror-TBA approach.
Abstract
Moving from the mirror theory Bethe-Yang equations proposed by Arutyunov and Frolov, we derive the thermodynamic Bethe Ansatz equations which should control the spectrum of the planar $\text{AdS}_5/\text{CFT}_4$ correspondence. The associated set of universal functional relations (Y-system) satisfied by the exponentials of the TBA pseudoenergies is deduced, confirming the structure inferred by Gromov, Kazakov and Vieira.