Analytic dc thermoelectric conductivities in holography with massive gravitons

Abstract

We provide an analytical derivation of the thermoelectric 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 for holographic models where momentum dissipation is realized through nontrivial scalars. The analytical approach confirms and supports the results found previously by means of numerical computations and the associated holographic renormalization procedure. Importantly, it also provides a precise identification of the range of validity of the hydrodynamic approximation.

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

“…First of all, the Wiedemann-Franz ratio κ DC /(σ DC T ) (where = π 2 /3. 25 Additionally, the thermal conductivityκ DC goes linearly to zero with the temperature 23 This formulae has been confirmed by our analytical computation in [23]. 24 We thank the referee for suggesting us this precise comparison and formulae.…”

“…More specifically, we have that the electric conductivity is temperature independent while the thermal conductivityκ DC goes linearly to 0 as T → 0 and is proportional to the heat capacity. 5 This remarkable behavior and the agreement of our formulae with those for Dirac fermions obtained in [1] are hints of the fact that, at least in the large-doping regime, massive gravity could possibly admit a quasi-particle description, even though a proof of this statement requires further detailed studies [41].…”

“…Actually, after the submission of the present paper, we obtained the DC thermo-electric transport coefficients also analytically [23]. However, the numerical method illustrated in the following sections is relevant by itself since it presents some interesting technical peculiarities and it is presently the only known method to compute the spectral behavior of the transport coefficients in massive gravity.…”

“…This fact, together with the many features which massive gravity has in common with the Fermi-liquid in this regime suggests that, at least in the large-doping region, a quasi-particle descriptions may be accurate. However, to prove the existence of a quasi-particle regime in the present model requires a systematic and careful analysis of the quasi-normal modes of the gravity solutions which we postpone to future investigations [41].…”

Momentum relaxation from the fluid/gravity correspondence

“…Secondly, since our description differs from that presented in [2], it is natural to revisit the motivating questions of that work. Through applying the fluid/gravity correspondence in a magnetic field we could construct a theory of magnetotransport [29][30][31][32] and study the frequency dependence of the Hall angle [33].…”