Weyl corrections to holographic conductivity

TL;DR

This paper investigates how higher-order Weyl tensor corrections in the bulk gravitational action affect the universal electrical conductivity and charge diffusion relations in holographic conformal field theories, revealing that these corrections break universality but are constrained by causality bounds.

Contribution

It introduces and analyzes the impact of Weyl tensor couplings on holographic transport properties, extending the understanding of universality violations in AdS/CFT correspondence.

Findings

Weyl corrections break the universal conductivity-charge diffusion relation.

Corrections are constrained by causality bounds in the boundary CFT.

The study provides bounds on transport parameters due to higher-derivative effects.

Abstract

For conformal field theories which admit a dual gravitational description in anti-de Sitter space, electrical transport properties, such as conductivity and charge diffusion, are determined by the dynamics of a U(1) gauge field in the bulk and thus obey universality relations at the classical level due to the uniqueness of the Maxwell action. We analyze corrections to these transport parameters due to higher-dimension operators in the bulk action, beyond the leading Maxwell term, of which the most significant involves a coupling to the bulk Weyl tensor. We show that the ensuing corrections to conductivity and the diffusion constant break the universal relation with the U(1) central charge observed at leading order, but are nonetheless subject to interesting bounds associated with causality in the boundary CFT.