Comments on the negative specific heat of the $T \bar T$ deformed symmetric product CFT

TL;DR

This paper investigates the negative specific heat phenomenon in $T ar T$ deformed conformal field theories, especially in symmetric product CFTs, linking it to phase transitions and thermodynamic properties.

Contribution

It demonstrates that $T ar T$ deformations lead to negative specific heat in certain CFTs and provides explicit thermodynamic calculations for symmetric product CFTs.

Findings

Negative specific heat occurs for $ ext{entropy} o E^eta$ with $eta > 1/2$.

Large $N$ symmetric product CFTs exhibit negative specific heat.

Negative specific heat indicates a first order phase transition when coupled to a heat bath.

Abstract

We show that the $T \bar T$ deformation of conformal field theories whose entropy grows as $S(E) \sim E^\gamma$ for $\gamma > 1/2$ exhibits negative specific heat in its microcanonical thermodynamic function $S({\cal E})$. We analyze the large $N$ symmetric product CFT as a concrete example of a CFT with this property and compute the thermodynamic functions such as $S({\cal E})$ and ${\cal E}(T)$. The negative specific heat in the microcanonical data is interpreted as signaling the first order phase transition when the system is coupled to a heat bath.