  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.
