Holographic Dissipative Properties of Non-relativistic Black Branes with Hyperscaling Violation

TL;DR

This paper explores the holographic properties of non-relativistic black branes with hyperscaling violation, deriving analytical expressions for transport coefficients that depend on temperature, and linking bulk metric exponents to boundary fluid behavior.

Contribution

It provides analytical calculations of transport coefficients for hyperscaling violating Lifshitz-like black branes, connecting bulk metric exponents to boundary fluid properties in a non-relativistic holographic model.

Findings

Transport coefficients scale as T^{3/2} for viscosity and conductivity.

DC resistivity scales as T^{-3/2}.

Results enhance understanding of strongly coupled systems like superconductors.

Abstract

In this work, we consider a class of hyperscaling violating Lifshitz-like black branes with metric scaling components $z=2$ and $\theta=-1$ whose corresponding holographic model can be treated as a non-relativistic fluid exhibiting Lifshitz-type symmetry. Having performed analytical calculations via the Klein-Gordon equation and the linear response theory, the experimental realizations of the concerned model, namely the transport coefficients, are found to behave as $\eta \propto T^{3/2}$, $\sigma_{DC} \propto T^{3/2}$, and $\rho_{DC} \propto T^{-3/2}$. The associated metric scaling exponents from the bulk theory are encrypted in the transport coefficients obtained for the holographic dual model. We believe that our analytical results can contribute to the endeavours in accomplishing a full understanding on the strongly coupled phenomena occurring in systems such as high temperature superconductors, the hypothetical magnetic monopoles, and liquid crystals.