Dissecting holographic conductivities

Abstract

Abstract:The DC thermoelectric conductivities of holographic systems in which translational symmetry is broken can be efficiently computed in terms of the near-horizon data of the dual black hole. By calculating the frequency dependent conductivities to the first subleading order in the momentum relaxation rate, we give a physical explanation for these conductivities in the simplest such example, in the limit of slow momentum relaxation. Specifically, we decompose each conductivity into the sum of a coherent contribution due to momentum relaxation and an incoherent contribution, due to intrinsic current relaxation. This decomposition is different from those previously proposed, and is consistent with the known hydrodynamic properties in the translationally invariant limit. This is the first step towards constructing a consistent theory of charged hydrodynamics with slow momentum relaxation.

Momentum relaxation from the fluid/gravity correspondence

“…Reassuringly, an identical structure to (3.19) was recently found in the 3+1 dimensional analogue of (2.1) through an explicit computation of the Green's functions of the boundary theory [19]. The fact that we precisely agree with these results is a strong check on the consistency of our hydrodynamical description.…”

“…In contrast at O(ε 0 ) there are differences and the results of [2] no longer apply. Very recently, a similar story was found to hold for the low-frequency AC conductivity of the 3+1 dimensional analogue of this theory [19]. Given the discussion so far in this paper, such discrepancies should not come as a surprise.…”

“…In particular there exist explicit black hole solutions to (2.1) when one applies the sources φ (0) A = kx A in the boundary. Various aspects of the thermodynamic and linear response coefficients of these solutions have been intensely studied in [11,19,26].…”

“…In particular, for a large class of theories it is now possible to obtain analytic expressions for all the DC conductivities in terms of horizon data [9,10,[14][15][16][17][18]. More recently, the low frequency AC conductivity has been calculated in a simple example by exploiting a clever decoupling of the bulk currents [19].…”

Magnetotransport from the fluid/gravity correspondence

“…Perhaps the most interesting aspects of these results are that holography provides, beyond leading order in the strength of momentum relaxation, a class of non-Drude models of transport (see for instance [10,11,[19][20][21][22]). Such models are likely to be necessary to describe the experimental measurements on strange metals [23][24][25].…”