Conductivities for Hyperscaling Violating Geometries

TL;DR

This work develops a unified scaling framework for holographic conductivities in hyperscaling-violating geometries by introducing two novel exponents, $\Phi$ (gauge-field scaling) and $\theta_m$ (matter sector scaling), in addition to the standard HV exponents $z$ and $\theta$. Using DBI probe-brane dynamics and careful holographic scaling arguments, the authors derive explicit scaling laws for DC and Hall conductivities at zero and finite temperature, and show how these match across D$d$/D$q$ constructions and Einstein-Maxwell-Dilaton systems. The approach clarifies how HV backgrounds control electromagnetic response and provides a phenomenological toolkit to model strange-metal transport, including predictions for thermoelectric coefficients. The results highlight that reproducing experimental trends may require distinct gauge-field scaling in different components or non-relativistic bulk sectors, offering concrete directions for connecting holographic models to real quantum-critical materials.

Abstract

We show that many results about holographic conductivities in geometries with hyperscaling violating scaling can be reproduced from simple scaling laws in the dual field theory. We show that the electro-magnetic response of probe branes in these systems require at least one additional scaling parameter Phi beyond the usual dynamical exponent z and hyperscaling violating exponent theta, as also pointed out in earlier work. We show that the scaling exponents can be chosen in such a way that the temperature dependence of DC conductivity and Hall angle in strange metals can be reproduced.