$T\bar T$, Black Holes and Negative Strings

TL;DR

This paper explores the effects of a $Tar T$-like deformation in string theory on $AdS_3$, revealing novel spacetime structures, black hole behaviors, and string dynamics, including singularities and upper energy bounds.

Contribution

It provides a detailed analysis of black holes and strings in a deformed $AdS_3$ spacetime with a singularity, highlighting the role of negative strings and the boundary theory implications.

Findings

Black hole size diverges near energy upper bound.

Fundamental strings pass through the singularity smoothly.

Spacetime exhibits a flipped signature beyond the singularity.

Abstract

String theory on $AdS_3$ has a solvable single-trace irrelevant deformation that is closely related to $T\bar T$. 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.