On string theory on deformed BTZ and $T\bar{T}$

Abstract

Aspects of superstring theory on deformed BTZ black holes, formed near $k$~NS5 branes by $p$~fundamental strings, and single-trace $T\bar{T}$ holography, are presented. The excitation energy of a singly wound long string plus its contribution to the energy of the black hole, $1/p$ fraction of the black-hole energy, is the same as that in $T\bar{T}$ deformed $CF{T}_2$ with $c=6k$. This supports the claim that the black hole can be thought of as a state in a symmetric product of $p$~$CF{T}_2$'s of central charge~$6k$, where the black-hole energy is split equally among all $p$ factors. A comment on superstring theory on deformed global $Ad{S}_3$ is also presented.