Abstract
We construct analytical Lifshitz massive black brane solutions in massive Einstein-Maxwell-dilaton gravity theory. We also study the thermodynamics of these black brane solutions and obtain the thermodynamical stability conditions. On the dual nonrelativistic boundary field theory with Lifshitz symmetry, we analytically compute the DC transport coefficients, including the electric conductivity, thermoelectric conductivity, and thermal conductivity. The novel property of our model is that the massive term supports the Lifshitz black brane solutions with $z\ensuremath{\ne}1$ in such a way that the DC transport coefficients in the dual field theory are finite. We also find that the Wiedemann-Franz law in this dual boundary field theory is violated, which indicates that it may involve strong interactions.
Highlights
In the study of the application of gauge-gravity duality [1,2,3] to condensed matter physics, the introduction of momentum relaxation plays an important role in the development of this research field because systems with momentum dissipation are more realistic
The DC conductivities in the dual boundary field theory are finite because z ≠ 1 causes the massive term in the action to survive
This observation in our model is novel because the usual Lifshitz black brane with z ≠ 1, which has no mechanism for momentum relaxation, cannot produce finite conductivities. (ii) In model II, when the Lifshitz exponent is z 1⁄4 1, the model reproduces the massive gravity proposed in [23] with the parameters α 1⁄4 0, β 1⁄4 β1, and F 1⁄4 m2 1⁄4 1
Summary
In the study of the application of gauge-gravity duality [1,2,3] to condensed matter physics, the introduction of momentum relaxation plays an important role in the development of this research field because systems with momentum dissipation are more realistic. It would be interesting to find the bulk sector to dually describe the momentum relaxation of a nonrelativistic boundary theory, which means we need to add ingredients into the bulk theory to introduce Lifshitz scaling and momentum dissipation To this end, we will construct Lifshitz black brane solutions in the massive Einstein-Maxwell-dilaton (EMD) gravity theory proposed in [28]. We note that the gravitational description of nonrelativistic theory with momentum relaxation has been studied in [16,38,39,40,41], where the authors introduced additional linear axion fields in the bulk to break the translation symmetry on the boundary, belonging to the first category involving momentum relaxation.
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