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

TL;DR

This paper explores topological phases in the hyperbolic plane, revealing fractional quantized indices in quantum Hall effects through noncommutative geometry and T-duality, and proposes a bulk-boundary correspondence model tailored to hyperbolic geometry.

Contribution

It introduces a model for fractional topological indices in hyperbolic spaces, extending Euclidean models and utilizing noncommutative geometry and T-duality techniques.

Findings

Fractional quantized indices can occur in hyperbolic topological phases.

A bulk-boundary correspondence model for fractional indices is proposed.

Hyperbolic geometry influences the topological properties and boundary phenomena.

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.