Momentum relaxation in holographic massive gravity

By R. Davison. 2013

263 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a5998f4bed055201ed522475d90dbb2f33da4bc1

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Citations in the corpus

A simple holographic model of momentum relaxation (2013, methodology): “Specifically the use of non-linear massive gravity theory of [12] was initiated in the holographic context by [13], and explored further in [14, 15].”
Dissecting holographic conductivities (2015, background): “The O(m̃2) term agrees with that of [21], as it should (given the similarities between the gravity theories under study here and there [14]).”
Thermodynamics of Black Holes in Massive Gravity (2014, background): “Some holographic consequence of the effect of graviton mass in massive gravity has been investigated in [21, 22, 23].”
Holographic metals and insulators with helical symmetry (2014, background): “The massive graviton approach was extended in [24, 25, 26] and provided for a formula for the DC conductivity in the context of massive gravity.”
Momentum dissipation and effective theories of coherent and incoherent transport (2014, methodology): “The parameter m acts as an effective mass for some of the metric fluctuations in the gravitational theory, and, for small m, is proportional to the momentum dissipation rate Γ ∼ m2/T [9].”
Thermoelectric DC conductivities from black hole horizons (2014, background): “The second paper, [36], calculates the thermoelectric response in the context of massive gravity, developing the work of [9, 10].”
Charge transport in holography with momentum dissipation (2014, background): “Unless the thermal pair creation contribution to the DC conductivity is parametrically larger than the dissipative term, we expect coherent transport with a sharp Drude peak (such as were seen in [12, 14, 15] for instance).”
Novel metals and insulators from holography (2014, result): “This latter type of behaviour was also seen in [11, 25] but, in contrast to what we find here, there it was in the context of non-vanishing entropy density and also with a temperature independent DC conductivity.”
Holographic Quantum Matter (2016, background): “Momentum relaxation through massive gravity was initially formulated on its own terms without gauge invariance [166; 716].”
Solid holography and massive gravity (2015, background): “Recently, a somewhat surprising connection between Condensed Matter (CM) and Massive Gravity (MG) has been unveiled: MG theories are especially relevant for CM applications by way of the AdS/CFT correspondence [1–4].”
The thermoelectric properties of inhomogeneous holographic lattices (2014, methodology): “For other work on the electric DC conductivity for various holographic black holes and using different approaches, see [11, 15–22].”
Universal Resistivity from Holographic Massive Gravity (2013, methodology): “Further aspects of both conductivity and hydrodynamics have been explored by Davison [16].”