Temperature quantization from the TBA equations

TL;DR

The paper investigates finite-size effects in the AdS5 × S5 superstring via the Thermodynamic Bethe Ansatz for the mirror model, linking cylinder circumference to inverse temperature and exploring Y-system analyticity. It shows that analytic Y-functions enforce quantized temperatures (integer or half-integer), and that both small-$h$ and large-$L$ regimes are consistent with generalized Lüscher formulas. A nonstandard analytic structure emerges: the Y-system is not analytic on the conventional plane, suggesting a formulation on an infinite-genus surface. This temperature quantization reveals a novel facet of the underlying $\mathfrak{psu}(2,2|4)$ symmetry and informs how finite-size effects relate to the AdS/CFT spectrum and potential orbifold interpretations in the gauge theory side.

Abstract

We analyze the Thermodynamic Bethe Ansatz equations for the mirror model which determine the ground state energy of the light-cone AdS_5 x S^5 superstring living on a cylinder. The light-cone momentum of string is equal to the circumference of the cylinder, and is identified with the inverse temperature of the mirror model. We show that the natural requirement of the analyticity of the Y-functions leads to the quantization of the temperature of the mirror model which has never been observed in any other models.