Momentum relaxation in holographic massive gravity

Abstract

We study the effects of momentum relaxation on observables in a recently proposed holographic model in which the conservation of momentum in the field theory is broken by the presence of a bulk graviton mass. In the hydrodynamic limit, we show that these effects can be incorporated by a simple modification of the energy-momentum conservation equation to account for the dissipation of momentum over a single characteristic timescale. We compute this timescale as a function of the graviton mass terms and identify the previously known "wall of stability" as the point at which this relaxation timescale becomes negative. We also calculate analytically the zero temperature AC conductivity at low frequencies. In the limit of a small graviton mass this reduces to the simple Drude form, and we compute the corrections to this which are important for larger masses. Finally, we undertake a preliminary investigation of the stability of the zero temperature black brane solution of this model, and rule out spatially modulated instabilities of a certain kind.

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

“…Comparing this expression with the electrical conductivity for a general hydrodynamic theory including the effects of impurity scattering (obtained in [16]), it was noted that the two expressions agree provided that the scattering rate τ −1 assumes the specific form 2) found in [14]. We will be later more precise about the explicit expression of the scattering rate.…”

“…In the condensed matter framework this kind of mechanism occurs, for example, in the presence of elastic electron scattering due to fixed impurities. The same model has been studied also in [14,15]; specifically, in [14], by analyzing the poles of the correlation functions in the hydrodynamic limit (namely at sufficiently low momentum dissipation rate τ −1 , where momentum is an almost conserved quantity), it was discussed that massive gravity is the dual gravitational JHEP09(2014)160 realization of a system in which the conservation law for the stress-energy tensor is…”

Magnetotransport from the fluid/gravity correspondence

“…For our choice of sources (2.6), this means that we will consistently ignore any terms in the constitutive relations proportional to u µ u ν ∂µφ (0) A ∂ν φ (0) B . 5 The only place the external field strength Fµν enters the equations of motions is through the vectorchannel constraint equation. That is the 3+1 dimensional analogue of equation (A.18) in [15].…”

“…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

“…Motivated by this goal, there has recently been a large amount of progress in calculating the transport properties of holographic models with broken translational invariance [4][5][6][7][8][9][10][11][12][13]. 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].…”