T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ and LST

Abstract

It was recently shown that the theory obtained by deforming a general two dimensional conformal theory by the irrelevant operator TT is solvable. In the context of holography, a large class of such theories can be obtained by studying string theory on AdS 3 . We show that a certain single trace TT deformation of the boundary CF T 2 gives rise in the bulk to string theory in a background that interpolates between AdS 3 in the IR and a linear dilaton spacetime in the UV, i.e. to a two dimensional vacuum of Little String Theory. This construction provides holographic duals for a large class of vacua of string theory in asymptotically linear dilaton spacetimes, and sheds light on the UV behavior of TT deformed CF T 2 . It may provide a step towards holography in flat spacetime.

A solvable irrelevant deformation of AdS3/CFT2

“…In this note we continue our study [1] of a certain deformation of string theory on AdS 3 . This study was motivated by two recent papers [2,3], which argued that perturbing a two dimensional conformal field theory (CFT 2 ) by a particular dimension (2, 2) operator, which behaves near the original CFT like the product of the holomorphic and anti-holomorphic components of the stress tensor, T T , leads to a well defined theory, despite the fact that it corresponds to a flow up the renormalization group (RG).…”

“…Moreover, the authors of these papers argued that the model is in a certain sense exactly solvable, and in particular computed its spectrum on IR × S 1 . An interesting property of the resulting spectrum is that it smoothly interpolates between an entropy associated with a CFT 2 in the IR, and one that exhibits Hagedorn growth in the UV [1].…”

“…In [1], we pointed out that there is a single trace deformation of string theory on AdS 3 that shares many elements with that of [2,3], but may be more interesting, since it modifies the local geometry of the bulk theory. Some of the features the two deformations have in common are:…”

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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].

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Background independent holographic dual to T T ¯ $$ T\overline{T} $$ deformed CFT with large central charge in 2 dimensions

“…For instance, the modification of the finite size energy spectrum for such theories can be computed [2,4]. From a holographic perspective, this deformation is also expected to modify the asymptotic behaviour of the bulk theory under consideration, see for instance [5]. The perspective I offer differs from this, because through the QRG mapping, this deformation is exactly what is needed to provide a kinetic term for the off shell ADM Hamiltonian constraint, which is an off-shell object.…”