Thermodynamics of $T \bar T$, $J \bar T$, $T \bar J$ deformed conformal field theories

TL;DR

This paper calculates the Hagedorn temperature in deformed conformal field theories using universal formulas and holographic methods, providing explicit expressions and connecting black hole thermodynamics to these deformations.

Contribution

It derives a closed-form expression for the Hagedorn temperature in $T ar T$, $J ar T$, $T ar J$ deformed CFTs and links holographic black hole thermodynamics to these deformations.

Findings

Explicit formula for Hagedorn temperature in deformed CFTs

Holographic computation of Hagedorn temperature in $AdS_3$ backgrounds

Identification of black hole configurations matching deformed thermodynamics

Abstract

We compute the Hagedorn temperature of $\mu T \bar T + \varepsilon_+ J \bar T + \varepsilon_-T \bar J$ deformed CFT using the universal kernel formula for the thermal partition function. We find a closed analytic expression for the free energy and the Hagedorn temperature as a function of $\mu$, $\varepsilon_+$, and $\varepsilon_-$ for the case of a compact scalar boson by taking the large volume limit. We also compute the Hagedorn temperature for the single trace deformed $AdS_3 \times S^1 \times T^3 \times S^3$ using holographic methods. We identify black hole configurations whose thermodynamics matches the functional dependence on $(\mu, \varepsilon_+, \varepsilon_-)$ of the double trace deformed compact scalars.