The Quantum Deformed Mirror TBA II

TL;DR

This paper explores the quantum deformed mirror thermodynamic Bethe ansatz for AdS_5 x S^5, deriving a Y-system that explicitly depends on excited states and boundary conditions, with a focus on asymptotic solutions and deformed Hubbard models.

Contribution

It introduces a novel Y-system for quantum deformed AdS/CFT, explicitly dependent on excited states and boundary conditions, and constructs its asymptotic solutions via twisted transfer matrices.

Findings

Derived the Y-system depending on excited states and boundary conditions.

Constructed the asymptotic solution using twisted transfer matrices.

Validated features at roots of unity, independent of deformation specifics.

Abstract

We discuss the description of generic excited states in the quantum deformed AdS_5 x S^5 mirror thermodynamic Bethe ansatz and derive the associated Y-system. This Y-system shows an interesting new feature; it depends explicitly on the excited state under consideration. Similarly, it also depends on twisted boundary conditions. We construct the asymptotic solution of these TBA and Y-system equations by deriving the twisted transfer matrix for the quantum deformed Hubbard model and finding the deformed mirror bound state dressing phase. This asymptotic construction is insensitive to the precise nature of the deformation, and thereby provides a nontrivial check of the interesting new features which arise precisely at roots of unity.