Electric-Magnetic Duality and Topological Insulators

摘要

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