Thermoelectric DC conductivities from black hole horizons

TL;DR

The paper addresses calculating DC thermoelectric and thermal conductivities in strongly coupled CFTs with momentum dissipation using holography. It develops a horizon-data framework by perturbing charged AdS black holes with constant electric fields and time-dependent heat sources, yielding analytic expressions for the DC transport matrix elements $\sigma$, $\alpha$, $\bar{\alpha}$, and $\bar{\kappa}$ in terms of horizon data, valid in D=4 and D=5. The authors illustrate the method on holographic Q-lattices and linear axion models, deriving low-temperature scalings and revealing thermal insulating behavior in certain ground states even when electric transport is metallic. These results provide a practical tool for diagnosing metallic versus insulating transport in strongly coupled systems and complement memory-matrix approaches in holography.

Abstract

An analytic expression for the DC electrical conductivity in terms of black hole horizon data was recently obtained for a class of holographic black holes exhibiting momentum dissipation. We generalise this result to obtain analogous expressions for the DC thermoelectric and thermal conductivities. We illustrate our results using some holographic Q-lattice black holes as well as for some black holes with linear massless axions, in both $D=4$ and $D=5$ bulk spacetime dimensions, which include both spatially isotropic and anisotropic examples. We show that some recently constructed ground states of holographic Q-lattices, which can be either electrically insulating or metallic, are all thermal insulators.