Thermoelectric DC conductivities in hyperscaling violating Lifshitz theories

Abstract

We analytically compute the thermoelectric conductivities at zero frequency (DC) in the holographic dual of a four dimensional Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically hyperscaling violating Lifshitz backgrounds with a dynamical exponent $z$ and hyperscaling violating parameter $\theta$. We show that the heat current in the dual Lifshitz theory involves the energy flux, which is an irrelevant operator for $z>1$. The linearized fluctuations relevant for computing the thermoelectric conductivities turn on a source for this irrelevant operator, leading to several novel and non-trivial aspects in the holographic renormalization procedure and the identification of the physical observables in the dual theory. Moreover, imposing Dirichlet or Neumann boundary conditions on the spatial components of one of the two Maxwell fields present leads to different thermoelectric conductivities. Dirichlet boundary conditions reproduce the thermoelectric DC conductivities obtained from the near horizon analysis of Donos and Gauntlett, while Neumann boundary conditions result in a new set of DC conductivities. We make preliminary analytical estimates for the temperature behavior of the thermoelectric matrix in appropriate regions of parameter space. In particular, at large temperatures we find that the only case which could lead to a linear resistivity $\rho \sim T$ corresponds to $z=4/3$.

49 pages; v2: minor corrections, references and a discussion of conductivity bounds added; v3 minor comments and two references added. Version published in JHEP

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• Quantum Critical Diffusion and Thermodynamics in Lifshitz Holography
• On the Rényi entropy of Lifshitz and hyperscaling violating black holes