Solvable time-like cosets and holography beyond $AdS$

We build a novel time-like coset sigma-model describing type-II superstring theory in a charged rotating black-brane background that interpolates between a locally $AdS_3$ in the IR and a linear-dilaton geometry in the UV. This allows one to perform a systematic study of holography in non-AdS backgrounds which are smoothly connected to $AdS_3$. We construct massless closed string states vertex operators in the NS-NS sector, calculate the corresponding two-point correlation functions, and discuss holographic interpretation of our results from 4+1 dimensional boundary field theory point of view. Compactifying the theory on $\mathbb{T}^4$, we show that the spectrum of a single long string with unit winding agrees with the spectrum of a CFT$_2$ deformed by $T\bar{T}$. We also calculate correlation functions of operators of the dual 1+1 dimensional non-conformal boundary field theory using world-sheet techniques.