Electric-Magnetic Duality and Topological Insulators

TL;DR

This paper explores the SL(2,Z) electric-magnetic duality in topological insulators, providing covariant expressions for optical effects and charges, and proposes a gravitational dual via AdS/CFT correspondence.

Contribution

It develops a duality framework for topological insulators with non-trivial electromagnetic parameters and introduces a gravitational dual description for strongly coupled cases.

Findings

SL(2,Z) covariant expressions for Faraday rotation

Clarification of induced charges in topological insulators

Proposal of a gravitational dual using AdS/CFT

Abstract

We work out the action of the SL(2,Z) electric-magnetic duality group for an insulator with a non-trivial permittivity, permeability and theta-angle. This theory has recently been proposed to be the correct low-energy effective action for topological insulators. As applications, we give manifestly SL(2,Z) covariant expressions for the Faraday rotation at orthogonal incidence at the interface of two such materials, as well as for the induced magnetic and electric charges, slightly clarifying the meaning of expressions previously derived in the literature. We also use electric-magnetic duality to find a gravitational dual for a strongly coupled version of this theory using the AdS/CFT correspondence.