Conductivity bounds in probe brane models

TL;DR

This paper establishes bounds on electrical conductivity in strongly coupled quantum field theories using holographic probe brane models, highlighting the effects of disorder and inhomogeneity across different dimensions.

Contribution

It derives simple upper and lower bounds on conductivity in probe brane models, including in the presence of disorder and in various spatial dimensions.

Findings

Bounds on conductivity are valid in arbitrary dimensions.

Both bounds persist in 2D even with bulk disorder.

Challenges exist in establishing bounds in higher dimensions with inhomogeneous metrics.

Abstract

We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is introduced entirely through an inhomogeneous background charge density, we find simple lower and upper bounds on the electrical conductivity in arbitrary dimensions. In field theories in two spatial dimensions, we show that both bounds persist even when disorder is included in the bulk metric. We discuss the challenges with finding sharp lower bounds on conductivity in three or more spatial dimensions when the metric is inhomogeneous.