Thermo-electric transport in gauge/gravity models with momentum dissipation

Abstract

We present a systematic definition and analysis of the thermo-electric linear response in gauge/gravity systems focusing especially on models with massive gravity in the bulk and therefore momentum dissipation in the dual field theory. A precise treatment of finite counter-terms proves to be essential to yield a consistent physical picture whose hydrodynamic and beyond-hydrodynamics behaviors noticeably match with field theoretical expectations. The model furnishes a possible gauge/gravity description of the crossover from the quantum-critical to the disorder-dominated Fermi-liquid behaviors, as expected in graphene.

Magnetotransport from the fluid/gravity correspondence

“…to all orders in our derivative expansion. 14 These observations are deeply connected to a beautiful recent paper by Donos and Gauntlett [34] (similar ideas have been developed in [35,48,49].). There it was shown that the DC conductivity of quite general holographic models can be understood from solving the forced Navier-Stokes equations for a fluid living on the black hole horizon.…”

“…Similarly, our expression for the fluid velocity, (4.9), is identical to that obtained by solving the Navier-Stokes equation on the horizon. We therefore see that the hydrodynamics of our boundary theory is precisely equivalent, in the DC limit, to that of 14 However, we certainly should expect that at higher orders in the derivative expansion we will see additional finite ω corrections to (3.8) and (4.3). 15 For inhomogeneous models the relationship between the boundary theory and the horizon physics is expected to be more complicated.…”

“…By finding ways to incorporate momentum relaxation into these models [1][2][3][4][5][6][7] rapid progress has been made in understanding their DC [8][9][10][11][12][13][14], and low-frequency [15][16][17][18][19] response coefficients.…”

Momentum relaxation from the fluid/gravity correspondence

“…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].…”

A simple holographic model of a charged lattice

“…There is also a broad class of effective models describing dissipative dynamics. An important example in this class is the massive gravity theory of [15][16][17][18][19]. In this theory, the graviton has an explicit mass term in the Lagrangian, and hence the translational invariance is absent.…”