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Letters in Mathematical Physics

, Volume 108, Issue 5, pp 1163–1201 | Cite as

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

  • Keith C. Hannabuss
  • Varghese Mathai
  • Guo Chuan Thiang
Article

Abstract

We state and prove a general result establishing that T-duality, or the Connes–Thom isomorphism, simplifies the bulk–boundary correspondence, given by a boundary map in K-theory, 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.

Keywords

T-duality Topological insulators Quantum Hall effect Defects Bulk–boundary correspondence Disorder Magnetic fields H-flux 

Mathematics Subject Classification

Primary 58B34 Secondary 46L80 53D22 81V70 

Notes

Acknowledgements

Varghese Mathai and Guo Chuan Thiang were supported by the Australian Research Council via ARC Discovery Project Grants DP150100008, FL170100020, and DE170100149, respectively. The authors thank the Erwin Schrödinger Institute (ESI), Vienna, for its hospitality during the ESI Program on Higher Structures in String Theory and Quantum Field Theory, when part of this research was completed.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Keith C. Hannabuss
    • 1
  • Varghese Mathai
    • 2
  • Guo Chuan Thiang
    • 2
  1. 1.Mathematical Institute, Andrew Wiles BuildingRadcliffe Observatory QuarterOxfordUnited Kingdom
  2. 2.Department of Pure Mathematics, School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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