Holography of Linear Dilaton Spacetimes from the Bottom Up

TL;DR

This paper explores the holographic properties of linear dilaton spacetimes, deriving effective field theories, analyzing correlators, and studying holographic fluids at finite temperature, revealing universal behaviors and potential dual theories.

Contribution

It develops a bottom-up holographic framework for linear dilaton backgrounds, connecting them to dual theories and analyzing their quantum and thermodynamic properties.

Findings

Holographic correlators exhibit singularities at specific kinematic thresholds.

Holographic fluid is pressureless across dimensions due to curvature-dilaton cancellation.

Universal temperature and Hagedorn behavior are found, matching known theories.

Abstract

The linear dilaton background is the keystone of a string-derived holographic correspondence beyond AdS$_{d+1}$/CFT$_d$. This motivates an exploration of the $(d+1)$-dimensional linear dilaton spacetime (LD$_{d+1}$) and its holographic properties from the low-energy viewpoint. We first notice that the LD$_{d+1}$ space has simple conformal symmetries, that we use to shape an effective field theory (EFT) on the LD background. We then place a brane in the background to study holography at the level of quantum fields and gravity. We find that the holographic correlators from the EFT feature a pattern of singularities at certain kinematic thresholds. We argue that such singularities can be used to bootstrap the putative $d$-dimensional dual theory using techniques analogous to those of the Cosmological Bootstrap program. Turning on finite temperature, we study the holographic fluid emerging on the brane in the presence of a bulk black hole. We find that the holographic fluid is pressureless for any $d$ due to a cancellation between Weyl curvature and dilaton stress tensor, and verify consistency with the time evolution of the theory. From the fluid thermodynamics, we find a universal temperature and Hagedorn behavior for any $d$. This matches the properties of a CFT$_2$ with large $T\overline T$ deformation, and of little string theory for $d=6$. Both the fluid equation of state and the spectrum of quantum fluctuations suggest that the $d$-dimensional dual theory arising from LD$_{d+1}$ is generically gapped.