$$ T\overline{T} $$ , black holes and negative strings

Abstract

String theory on AdS3 has a solvable single-trace irrelevant deformation that is closely related to $$ T\overline{T} $$ T T ¯ . For one sign of the coupling, it leads to an asymptotically linear dilaton spacetime, and a corresponding Hagedorn spectrum. For the other, the resulting spacetime has a curvature singularity at a finite radial location, and an upper bound on the energies of states. Beyond the singularity, the signature of spacetime is flipped and there is an asymptotically linear dilaton boundary at infinity. We study the properties of black holes and fundamental strings in this spacetime, and find a sensible picture. The singularity does not give rise to a hard ultraviolet wall for excitations -one must include the region beyond it to understand the theory. The size of black holes diverges as their energy approaches the upper bound, as does the location of the singularity. Fundamental strings pass smoothly through the singularity, but if their energy is above the upper bound, their trajectories are singular. From the point of view of the boundary at infinity, this background can be thought of as a vacuum of Little String Theory which contains a large number of negative strings.

Holographic complexity of LST and single trace $$ T\overline{T} $$

“…U 1/ √ kλ) to AdS 3 . The smooth interpolation between R 1,1 × R φ in the UV to AdS 3 in the IR corresponds to interpolation between near horizon geometry of the NS5 brane system to that of the F1 strings [28,74]. The spacetime theory interpolates between a CFT 2 with central charge 6kp in the IR to two-dimensional LST in the UV.…”

“…Both these properties are very similar to local quantum field theories. For a detailed review of LST see [18,19] The above discussion has a simple generalization to backgrounds at finite temperature [22,74,76]:…”

Entanglement entropy for $$ \mathrm{T}\overline{\mathrm{T}} $$, $$ \mathrm{J}\overline{\mathrm{T}} $$, $$ \mathrm{T}\overline{\mathrm{J}} $$ deformed holographic CFT

“…Let us begin by considering type II string theory on R 1,4 × S 1 × T 4 with a stack of k NS5 branes wrapping S 1 × T 4 and p F1 strings stretched along the S 1 [21]. As is often done in Little String Theory (LST), the decoupled theory on the NS5 branes are obtained by setting the asymptotic string coupling g ∞ → 0 and focusing at distances of the order g ∞ l s from the NS5 branes where l s is the string length [22].…”

“…The condition µ > 0 stems from the requirement that the spectrum for ε + = ε − = 0 is regular in the UV. (See however [13,21] for discussions on violating this bound.) The condition µ−4 + − = 0 stems from the requirement that the y cycle be spacelike [1].…”

$$ T\overline{T} $$ and $$ J\overline{T} $$ deformations in quantum mechanics

“…For other holographic proposals and their generalizations, see[4,5,[8][9][10]]. 2 In this paper, by abuse of language, we will keep referring to these deformations in d > 2 and in d = 1 as the T T deformation, similarly for JT and their general linear combinations.…”