Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
Gleb Arutyunov, Sergey Frolov
TL;DR
The paper derives a comprehensive set of Thermodynamic Bethe Ansatz equations for the AdS5 x S5 mirror theory using the string hypothesis and thermodynamic limit, enabling a structured route to the finite-size spectrum and the associated Y-system. It formulates densities for all excitations, performs a free-energy minimization to obtain pseudo-energy equations, and then recasts the system into a local Y-system within a limited rapidity domain. The work highlights pivotal unresolved issues, notably the mirror dressing phase and the analytic continuation needed for excited states, and discusses how its results compare to other contemporary derivations. Together, these advances push toward a complete solution of the AdS/CFT spectral problem by providing a rigorous TBA framework tailored to the AdS5 x S5 mirror model.
Abstract
We use the string hypothesis for the mirror theory to derive the Thermodynamic Bethe Ansatz equations for the AdS_5 x S^5 mirror model. We further demonstrate how these equations can be used to construct the associated Y-system recently discussed in the literature, putting particular emphasis on the assumptions and the range of validity of the corresponding construction.