Abstract
We consider a gravitational theory with two Maxwell fields, a dilatonic scalar and spatially dependent axions. Black brane solutions to this theory are Lifshitz-like and violate hyperscaling. Working with electrically charged solutions, we calculate analytically the holographic DC conductivities when both gauge fields are allowed to fluctuate. We discuss some of the subtleties associated with relating the horizon to the boundary data, focusing on the role of Lifshitz asymptotics and the presence of multiple gauge fields. The axionic scalars lead to momentum dissipation in the dual holographic theory. Finally, we examine the behavior of the DC conductivities as a function of temperature, and comment on the cases in which one can obtain a linear resistivity.
Highlights
Are of a clear technical advantage, as they lead to remarkable simplifications in the analysis
We examine the possible temperature behaviors allowed by our model, and identify some of the parameter choices that can lead to a linear resistivity, for both Lifshitz and AdS asymptotics
In an attempt to gain insight into strongly coupled phases with anomalous scalings, we have chosen to work with an holographic model that gives rise to non-relativistic geometries that violate hyperscaling
Summary
We shall consider a particular case amongst the class of theories described in appendix A, in which we specialise to four-dimensional gravity coupled to two Maxwell fields, a dilaton and two axions. The theory described by (2.1) admits Lifshitz-like, hyperscaling violating black brane solutions, given by. The solution reduces to the Lifshitz-like vacuum when these parameters vanish. The solution is asymptotically Lifshitz-like with hyperscaling violation. It should be noted that the two Maxwell fields play very different roles in the black hole solution. In. particular, its “charge” Q1 is fixed, for given Lifshitz and hyperscaling violating exponents z and θ, and the solution becomes asymptotically AdS if Q1 = 0. For reasons that will become apparent shortly, and to make contact with some of the literature, we would like to parametrize the scalings of the two gauge fields in terms of two exponents ζ1 and ζ2, the analogs of the conduction exponent ζ that controls the anomalous scaling dimension of the charge density operator [31,32,33].
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