Temperature quantization from the TBA equations

TL;DR

This paper investigates the Thermodynamic Bethe Ansatz equations for the mirror model of the AdS_5 x S^5 superstring, revealing a novel temperature quantization condition arising from analyticity constraints.

Contribution

It introduces the concept of temperature quantization in the mirror model, a phenomenon not previously observed in similar integrable systems.

Findings

Temperature of the mirror model is quantized due to analyticity of Y-functions.

The quantization condition links the physical parameters of the superstring to discrete temperature values.

This discovery provides new insights into the integrable structure of the AdS/CFT correspondence.

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.