Holography and Irrelevant Operators

TL;DR

This paper investigates three-dimensional holographic spacetimes with linear dilaton asymptotics, connecting supergravity solutions to $T ar{T}$-deformed conformal field theories, and explores their properties and stability.

Contribution

It presents explicit supergravity solutions interpolating between BTZ black holes and linear dilaton or flat spacetimes, linking gravity parameters to field theory deformations.

Findings

Solutions exhibit $T ar{T}$-like square root structure.

Mass calculations agree with the $T ar{T}$ formula for non-spinning black holes.

Discussion of potential instabilities due to closed string tachyons.

Abstract

We explore the holographic proposal involving spacetimes with linear dilaton asymptotics in three dimensions from a gravity perspective. The holographic dual shares some properties with a symmetric product conformal field theory deformed by a single-trace analogue of the $T \overline{T}$ deformation. We present solutions of ten-dimensional supergravity which interpolate from BTZ black holes in the interior to either a linear dilaton spacetime near infinity, or to flat space. This allows a precise identification of field theory parameters with gravity parameters. The solutions manifestly exhibit the square root structure that is characteristic of $T \overline{T}$-deformed conformal field theories. We compute the mass of the spacetimes using the covariant phase space formalism and find agreement with the square root formula for the case of black holes without spin. We also discuss whether closed string tachyons might play a role when the deformation parameter becomes too large and the vacuum becomes unstable.