Holography of linear dilaton spacetimes from the bottom up

The linear dilaton (LD) 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 TT <overline> deformation, and of little string theory for d = 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 LD d + 1 is generically gapped.