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

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.

33 pages, 2 figures, minor revision

References in corpus (3)

• Helical Metal Inside a Topological Band Insulator
• Observation of Dirac Monopoles in a Synthetic Magnetic Field
• Differential topology of semimetals

Cited by in corpus (11)

• The $K$-theoretic bulk-edge correspondence for topological insulators
• Bulk-boundary correspondence for disordered free-fermion topological phases
• Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• Chiral Flow in One-dimensional Floquet Topological Insulators
• Index theory and topological phases of aperiodic lattices
• Bulk-edge correspondence and the cobordism invariance of the index
• Crystallographic T-duality
• Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices
• T-duality and the bulk-boundary correspondence
• Exact sequence between real and complex bivariant K theories and application to the Z2 pairing