T-duality simplifies bulk-boundary correspondence: the noncommutative case

TL;DR

This paper proves that T-duality transforms the complex bulk-boundary correspondence into a straightforward geometric restriction, simplifying analysis in various physical and mathematical contexts including string theory and condensed matter physics.

Contribution

It establishes a general theorem showing T-duality simplifies the bulk-boundary correspondence to a geometric restriction map across multiple settings.

Findings

T-duality converts bulk-boundary correspondence into a geometric restriction

The result applies in arbitrary dimensions and in real and complex cases

It holds even with disorder, magnetic fields, and H-flux

Abstract

We state and prove a general result establishing that T-duality simplifies the bulk-boundary correspondence, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors, and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to String Theory and to the study of the quantum Hall effect and topological insulators with defects in Condensed Matter Physics.