Abstract
In this paper we prove the equivalence among (i) the weakly coupled worldsheet string theory described by the coset sigma model frac{mathrm{SL}{left(2,mathrm{mathbb{R}}right)}_ktimes mathrm{U}(1)}{mathrm{U}(1)} × S3 × T4 with SL(2, ℝ) WZW level k ≥ 2, (ii) the full near horizon theory of the NS5 branes with k NS5 branes wrapping T4 × S1, p » 1 F1 strings wrapping S1 and n units of momentum along the S1 and (iii) the single trace Toverline{T} deformation of string theory in AdS3 × S3 × T4. As a check we compute the spectrum (continuous) of the spacetime theory by performing BRST quantization of the coset description of the worldsheet theory and show that it matches exactly with the one derived in the case of single trace Toverline{T} deformed string theory in AdS3. Secondly, we compute the two-point correlation function of local operators of the spacetime theory using the worldsheet coset approach and reproduce the same two-point function from the supergravity approach.
Highlights
In this paper we prove the equivalence among (i) the weakly coupled worldsheet string theory described by the coset sigma model
The background geometry interpolates between a BTZ black hole in the IR, that is described by a particular orbifold sigma model on SL(2,R) Γ
In this paper we argue that the gauged WZW model with the gauge currents given by describes the full interpolating bulk geometry both at zero and finite temperature
Summary
We will briefly review certain aspects of superstrings in AdS3 and its single trace T T deformation which we will use heavily later in the sections that follow. For more detailed discussion of string theory in AdS3, we will refer to the reader the following references [27,28,29,30,31,32]
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