Non-linear asymptotic symmetries in warped AdS$_3$ holography

TL;DR

This paper investigates the asymptotic symmetries of warped AdS$_3$ backgrounds, revealing a non-linear algebra that linearizes to a structure matching $J\bar{T}$-deformed CFTs, advancing understanding of holography beyond AdS.

Contribution

It computes the asymptotic symmetry algebra of a specific warped BTZ background, showing it matches the symmetry of a symmetric product orbifold of $J\bar{T}$-deformed CFTs.

Findings

The asymptotic symmetry algebra is a non-linear Poisson algebra.

After redefinition, the algebra linearizes to two copies of Virasoro and $U(1)$ Kac-Moody.

The algebra matches the symmetry of a symmetric product orbifold of $J\bar{T}$-deformed CFTs.

Abstract

Warped AdS$_3$ backgrounds provide set-ups to study holography beyond AdS and, in particular, holography for near-extremal Kerr black holes. A certain $U(1)$ charged warped BTZ background supported by pure NS-NS flux was constructed in string theory in arXiv:2111.02243. While older works found, in absence of $U(1)$ charges, that the warped black holes' thermal entropy obeys a Cardy formula, the addition of $U(1)$ charges in arXiv:2111.02243 leads to the universal entropy formula in a $J\bar{T}$-deformed CFT and not to the charged Cardy formula. In this article, we explore further the implications of this result for warped AdS$_3$ holography. We compute the asymptotic symmetries of the warped BTZ background of arXiv:2111.02243 and obtain an infinite-dimensional non-linear Poisson algebra that can be linearized, after a non-linear redefinition of generators, to two commuting copies of the $(Virasoro\times U(1)Kac-Moody)$ algebra. The algebra matches the symmetry algebra of a symmetric product orbifold of $J\bar{T}$-deformed CFTs. We contrast the results with those for a similar warped BTZ background supported by both NS-NS and RR flux.