Holographic thermal DC response in the hydrodynamic limit

Abstract

We consider black hole solutions of Einstein gravity that describe deformations of CFTs at finite temperature in which spatial translations have been broken explicitly. We focus on deformations that are periodic in the non-compact spatial directions, which effectively corresponds to considering the CFT on a spatial torus with a non-trivial metric. We apply a DC thermal gradient and show that in a hydrodynamic limit the linearised, local thermal currents can be determined by solving linearised, forced Navier-Stokes equations for an incompressible fluid on the torus. We also show how sub-leading corrections to the thermal current can be calculated as well as showing how the full stress tensor response that is generated by the DC source can be obtained. We also compare our results with the fluid-gravity approach.arXiv:1609.08912v2 [hep-th]

Pinning of longitudinal phonons in holographic spontaneous helices

“…We remove the gauge redundancy 16 For a hydrodynamic-like framework where the momentum relaxation is taken into account consistently see e.g. [82][83][84] where the symmetry is broken explicitly by spatial dependent scalar fields, by chemical potential [85] and by curved background metric [86,87]. Following [37], we implement this by adding the terms ∇ (µ τ g ν) , ∇ µ τ A , ∇ µ τ B to the Einstein and Maxwell equations, respectively, with the appropriate coefficients.…”

Holographic DC conductivity and Onsager relations

“…In order to introduce suitable DC sources for the electric and heat currents we consider the following linear perturbation of the black hole solution 6 :…”

“…While these hydrostatic fluid equations, which we refer to as Stokes equations, can be used to extract the DC conductivities, in general they are only indirectly related to physical quantities in the dual field theory. However, in the special situation of the hydrodynamic limit of the holographic lattice, in which the temperature is the highest scale, one can show that the horizon fluid corresponds to the hydrodynamical fluid of the dual field theory in the presence of external DC electric fields and thermal gradients [6], thus making contact with the work on fluid-gravity [7].…”

Hydrodynamic charge and heat transport on inhomogeneous curved spaces

“…Using the spectral methods of [7], described in Appendix B, we have numerically solved (14) with the equations of state (19), in inhomogeneous chemical potentials and metrics. We have always taken periodic boundary conditions, and assumed that the metric disorder and chemical potential disorder are uncorrelated, for simplicity.…”

“…Our formalism is relatively similar to the emergent "hydrodynamic" formalism used to describe transport in strongly correlated systems described via the AdS/CMT correspondence[4,15,16,17,18]. However, in most of these papers, the random spatial metric is an emergent phenomenon from the point of view of the bulk description of the field theory -the exception is[19]. We emphasize that we are interested in scenarios where the inhomogeneous spatial metric is a physical effect.…”