Holography of linear dilaton spacetimes from the bottom up

Abstract

The linear dilaton (LD) background is the keystone of a string-derived holographic correspondence beyond AdSdþ1=CFTd. This motivates an exploration of the (d þ 1)-dimensional linear dilaton spacetime (LDdþ1) and its holographic properties from the low-energy viewpoint.We first notice that the LDdþ1 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 CFT2 with large TT¯ deformation, and of little string theory for d ¼ 6. We also find that the holographic fluid entropy exactly matches the bulk black hole Bekenstein-Hawking entropy. Both the fluid equation of state and the spectrum of quantum fluctuations suggest that the d-dimensional dual theory arising from LDdþ1 is generically gapped.