A solvable irrelevant deformation of AdS3/CFT2

Abstract

Recently we proposed a universal solvable irrelevant deformation of AdS 3 /CFT 2 duality, which leads in the ultraviolet to a theory with a Hagedorn entropy [1]. In this note we provide a worldsheet description of this theory as a coset CFT, and compare its spectrum to the field theory predictions of [2,3].

$$ T\overline{T} $$ type deformation in the presence of a boundary

“…The irrelevant deformation studied in [20] shares some qualitative features with the original TT -deformation of [1,2], in particular, the property of being solvable and universal [21]. The model of [20], however, follows from a rather different approach.…”

“…The deformation (2.2) does break SL(2, R) symmetry but is exactly marginal in the sense that it preserves conformal invariance. The deformation is still solvable in the sense that the spectrum and correlation functions can be exactly derived for finite λ 0 [21][22][23].…”

“…This yields a solvable deformation of AdS 3 /CFT 2 duality, which leads to a theory with a Hagedorn entropy in the UV. The spectrum of the theory can be explicitly obtained and compared with the spectrum predicted in [1,2]; this was done in [21]. Correlation functions for the model of [20] on the sphere topology were also computed [22,23] which led to interesting observations about the theory, especially in relation to its non-locality.…”

“…y ≥ 0 with z = x + iy, while the boundary will be given by the real line z = x. Bulk action S = S WZW +S D has been studied in detail in [20][21][22][23][24], and it appeared in the literature before in different contexts; see for instance [25]. In the case λ 0 = 0 it corresponds to the SL(2, R) WZW model, which describes the string σ-model on AdS 3 ; see [26] and references therein and thereof.…”

“…where λ 0 is defined by integrating Φ 1 over the worldhseet, and boundary terms have been dismissed; see [20,21] for details. The single integration over the worldsheet variable in (2.5) explains in what sense this operator can be regarded as a single trace version of (2.4).…”