Root-$T\overline{T}$ deformed CFT partition functions at large central charge
Abstract
In this work, we investigate the partition function of 2d CFT under root- deformation. We demonstrate that the deformed partition function satisfies a flow equation. At large central charge sector, the deformed partition function reduces to a redefinition of the modular parameters, which preserves modular invariance under the deformed parameters. We then derive a Cardy-like formula for the asymptotic density of states using modular bootstrap trick. In the context of AdS/CFT, it was proposed the root- deformed CFT corresponds to the AdS with certain deformed boundary condition. We show the deformed BTZ black hole is a quotient of hyperbolic space. In terms of Chern-Simons formulation, we compute the root- deformed BTZ black hole entropy and find that it obeys a Cardy-like formula, which is consistent with the modular bootstrap result. Furthermore, employing the Wilson spool technique, we compute the one-loop partition functions for the root- deformed AdS geometry. Our results reveal an exact match between one-loop gravitational partition function and the large expansion of root- deformed CFT partition function.
Cite
@article{arxiv.2505.12093,
title = {Root-$T\overline{T}$ deformed CFT partition functions at large central charge},
author = {Miao He},
journal= {arXiv preprint arXiv:2505.12093},
year = {2025}
}
Comments
37 pages, v2: references added,v3: minor revision, published version