  A solvable irrelevant deformation of AdS$_3$/CFT$_2$ correspondence leading
to a theory with Hagedorn spectrum at high energy has been recently proposed.
It consists of a single trace deformation of the boundary theory, which is
inspired by the recent work on solvable $T\bar{T}$ deformations of
two-dimensional CFTs. Thought of as a worldsheet $\sigma $-model, the
interpretation of the deformed theory from the bulk viewpoint is that of string
theory on a background that interpolates between AdS$_3$ in the IR and a linear
dilaton vacuum of little string theory in the UV. The insertion of the operator
that realizes the deformation in the correlation functions produces a
logarithmic divergence, leading to the renormalization of the primary
operators, which thus acquire an anomalous dimension. We compute this anomalous
dimension explicitly, and this provides us with a direct way of determining the
spectrum of the theory. We discuss this and other features of the correlation
functions in presence of the deformation.
