Non-linear asymptotic symmetries in warped AdS3 holography

A bstract 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 [JHEP 04 (2022) 177]. 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 [JHEP 04 (2022) 177] leads to the universal entropy formula in a $$ J\overline{T} $$ J 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 [JHEP 04 (2022) 177] 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 × U (1) Kac – Moody ) algebra. The algebra matches the symmetry algebra of a symmetric product orbifold of $$ J\overline{T} $$ J T ¯ -deformed CFTs, up to central terms. We contrast the results with those for a similar warped BTZ background supported by both NS-NS and RR flux.