Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 3

Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence

Pages: 803 – 840

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n3.a5

Authors

Varghese Mathai (Department of Pure Mathematics, School of Mathematical Sciences, University of Adelaide, SA, Australia)

Guo Chuan Thiang (Department of Pure Mathematics, School of Mathematical Sciences, University of Adelaide, SA, Australia)

Abstract

We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models used in the Euclidean setting, a model for the bulk-boundary correspondence of fractional indices is proposed, guided by the geometry of hyperbolic boundaries.

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Published 4 December 2019