TT¯ deformed partition functions

Abstract

We demonstrate the presence of modular properties in partition functions of TT 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 TT flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.