$T\bar{T}$-deformations, AdS/CFT and correlation functions

Abstract

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.

17 pages. v3 references and comments added. Version to appear in JHEP

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