Topological Insulators and Superconductors from String Theory

TL;DR

This paper establishes a deep connection between topological insulators/superconductors and string theory by linking their classifications via D-branes and K-theory, and explores their gauge theories and holographic realizations.

Contribution

It demonstrates a one-to-one correspondence between K-theory classifications of topological phases and D-brane charges in string theory, providing a string-theoretic framework for topological matter.

Findings

D-branes classify topological insulators/superconductors via K-theory.

String theory naturally incorporates gauge interactions with topological terms.

Holographic models of topological phases emerge from multiple D-branes.

Abstract

Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and supercondutors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K-theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K-theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the $\theta$-term in various dimensions. This sheds light on topological insulators and superconductors 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. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).