Spectral equations and ground state for the modular $\sinh$-Gordon model

Abstract

We study the modular pair of $TQ$ equations for the quantum $\sin$-Gordon model in the framework of non-compact ${\mathcal{U}}_{q,q^{\ast }}({\widehat{sl}}_2)$. We assume some conjectures for the thermodynamic limit allowing one to obtain its ground state.