A bstract We demonstrate the presence of modular properties in partition functions of TT̄ T 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 TT̄ T T ¯ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.
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Datta et al. (2018) studied this question.
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