Analytic DC thermo-electric conductivities in holography with massive gravitons

TL;DR

The paper addresses DC thermo-electric transport in holographic models with momentum dissipation implemented by a bulk graviton mass. It applies the Donos-Gauntlett membrane paradigm to derive analytic expressions for the DC conductivities, confirming prior numerical results. Key results include explicit forms sigmaDC, sDC, and kappaDC in terms of thermodynamic quantities and a momentum-relaxation timescale tau, e.g., sigmaDC = 1/q^2 + (rho^2)/(E+P) tau, sDC = (S rho)/(E+P) tau, and kappaDC = (S^2 T)/(E+P) tau. These findings establish the hydrodynamic regime's validity, clarify holographic renormalization with finite counter-terms, and provide a solid analytic foundation for earlier numerical work.

Abstract

We provide an analytical derivation of the thermo-electric transport coefficients of the simplest momentum-dissipating model in gauge/gravity where the lack of momentum conservation is realized by means of explicit graviton mass in the bulk. We rely on the procedure recently described by Donos and Gauntlett in the context of Q-lattices and holographic models where momentum dissipation is realized through non-trivial scalars. The analytical approach confirms the results found previously by means of numerical computations.