Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

A bstract We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in context of generalized T $$ \overline{\mathrm{T}} T ¯ deformations. focus on sinh-Gordon model and its elliptic deformation both fermionic bosonic realizations. confirm that determining factor a turning point TBA, interpreted as finite Hagedorn temperature, is difference between number bound states resonances theory. Implementing numerical pseudo-arclength continuation method, we are able to follow solutions TBA equations past all way ultraviolet regime. find any k pair complex conjugate below such effective central charge minimized. As ? ? UV goes zero model. Finally uncover new family complete theories defined by counterparts S -matrices describing ? 1 , 3 non-unitary minimal models \mathcal{M} M 2 n +3 .