# T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases

@article{Mathai2015TDualitySB, title={T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases}, author={Varghese Mathai and Guo Chuan Thiang}, journal={Annales Henri Poincar{\'e}}, year={2015}, volume={17}, pages={3399-3424} }

Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality transforms the bulk–boundary homomorphism into a simpler restriction map in two dimensions. In this paper, we partially generalize these results to higher dimensions in both the complex and real cases, and briefly discuss the 4D quantum Hall effect.

## 22 Citations

### T-duality trivializes bulk-boundary correspondence: the parametrised case

- Mathematics
- 2015

We state a general conjecture that T-duality trivialises a model for the bulk-boundary correspondence in the parametrised context. We give evidence that it is valid by proving it in a special…

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

- Physics
- 2016

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…

### T-duality of topological insulators

- Mathematics, Physics
- 2015

Topological insulators and D-brane charges in string theory can both be classified by the same family of groups. In this paper, we extend this connection via a geometric transform, giving a novel…

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

- MathematicsAdvances in Theoretical and Mathematical Physics
- 2019

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…

### The K-Theoretic Bulk–Edge Correspondence for Topological Insulators

- Mathematics
- 2016

We study the application of Kasparov theory to topological insulator systems and the bulk–edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge…

### A non-commutative framework for topological insulators

- Mathematics, Physics
- 2016

We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of non-commutative…

### ‘Real’ Gerbes and Dirac Cones of Topological Insulators

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2021

A time-reversal invariant topological insulator occupying a Euclidean half-space determines a ‘Quaternionic’ self-adjoint Fredholm family. We show that the discrete spectrum data for such a family is…

### Controlled Topological Phases and Bulk-edge Correspondence

- Mathematics
- 2015

In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with…

### Bulk-Boundary Correspondence for Disordered Free-Fermion Topological Phases

- MathematicsCommunications in Mathematical Physics
- 2019

Guided by the many-particle quantum theory of interacting systems, we develop a uniform classification scheme for topological phases of disordered gapped free fermions, encompassing all symmetry…

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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…

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We state a general conjecture that T-duality trivialises a model for the bulk-boundary correspondence in the parametrised context. We give evidence that it is valid by proving it in a special…

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