Band spectrum is D-brane

TL;DR

This paper establishes a novel connection between the band spectrum of topological insulators and D-branes in string theory, linking condensed matter physics with string theoretical constructs through geometric and topological methods.

Contribution

It introduces a new perspective by identifying the band spectrum as D-branes and relates edge states to noncommutative monopoles, bridging condensed matter and string theory.

Findings

Band spectrum corresponds to D-brane shapes.

Edge states are D-branes representing noncommutative monopoles.

Berry connection relates to D-brane configurations.

Abstract

We show that band spectrum of topological insulators can be identified as the shape of D-branes in string theory. The identification is based on a relation between the Berry connection associated with the band structure and the ADHM/Nahm construction of solitons whose geometric realization is available with D-branes. We also show that chiral and helical edge states are identified as D-branes representing a noncommutative monopole.