Abstract
A solvable irrelevant deformation of AdS3/CFT2 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 Toverline{T} deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 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.
Highlights
Spectrum in the ultraviolet (UV), which would be dual to the linear dilaton background
Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV
Large k regime corresponds to the limit in which the string length scale α is small in comparison with the radius of the AdS3 space(s). This type of AdS3 solution to string theory has been extensively studied in the literature [10,11,12,13,14,15] and it represents one of the few examples in which holography can be explored beyond the supergravity approximation, allowing to have access to purely stringy effects
Summary
The deformation proposed in [1], which interpolates between the IR CFT2 and the UV non-local theory, is given by an irrelevant operator built out of the holomorphic and antiholomorphic components of the boundary CFT2 stress tensor written down in [11]. In order to understand what operator (2.1) means from the dual theory point of view, recall that the zero mode of the local current J− (and J−) corresponds in the boundary IR CFT to the SL(2, R) generator L−1 Λ is the coupling λ0 dressed by a factor This argument is unjustifiably fast, as the insertion of the operator D in the 2-point function produces a logarithmic singularity and leads to the renormalization of the vertex operators, which acquire an anomalous dimension. We will explain how the method used here to compute the 2-point correlation function can be applied to compute higher-point correlation functions in the deformed CFT
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