$T\bar{T}$ deformed partition functions

TL;DR

This paper explores the modular properties of partition functions in $T\bar{T}$ deformed conformal field theories, revealing insights into their spectrum, density of states, and holographic implications.

Contribution

It demonstrates the modular properties of $T\bar{T}$ deformed partition functions and analyzes their effects on the spectrum and holography.

Findings

Partition functions exhibit modular properties after $T\bar{T}$ deformation.

The density of states interpolates between Cardy and Hagedorn behaviors.

A sub-sector remains undeformed under the $T\bar{T}$ flow.

Abstract

We demonstrate the presence of modular properties in partition functions of $T\bar{T}$ deformed conformal field theories. These properties are verified explicitly for the deformed free boson. The modular features facilitate a derivation of the asymptotic density of states in these theories, which turns out to interpolate between Cardy and Hagedorn behaviours. We also point out a sub-sector of the spectrum that remains undeformed under the $T\bar{T}$ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.