$T\bar{T}$ deformed partition functions

Understand

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.