Topological Insulators and Superconductors from D-branes

TL;DR

This paper proposes a string theory framework using D-branes to realize and classify topological insulators and superconductors, connecting topological phases with D-brane charges and gauge theories.

Contribution

It establishes a direct correspondence between K-theory classification of TIs/TSCs and D-brane charges, providing a novel string theory perspective on topological phases.

Findings

D-brane charges correspond to topological insulator classifications

Gauge interactions naturally emerge in the string theory realization

Includes models like the honeycomb lattice Kitaev model and its extensions

Abstract

Realization of topological insulators (TIs) and superconductors (TSCs), such as the quantum spin Hall effect and the Z_2 topological insulator, in terms of D-branes in string theory is proposed. We establish a one-to-one correspondence between the K-theory classification of TIs/TSCs and D-brane charges. The string theory realization of TIs and TSCs comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature. This sheds light on TIs and TSCs beyond non-interacting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions.