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. 
View on Springer
arxiv.org
22 Citations
Highly Influential Citations
2
Background Citations
12
Methods Citations
4

22 Citations

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

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

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 and the bulk-boundary correspondence

T-duality of topological insulators

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

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

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

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

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

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

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…

References

SHOWING 1-10 OF 66 REFERENCES

T-duality trivializes bulk-boundary correspondence

Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum…

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

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…

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

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 of topological insulators

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…

D-branes, T-duality, and Index Theory

We show that the transformation of D-branes under T-duality on four-torus is represented by Nahm transform of instantons. The argument for this allows us to generalize Nahm transform to the case of…

The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory

We prove the bulk-edge correspondence in K-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This…

Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics

Illustration of key concepts in dimension d = 1.- Topological solid state systems: conjectures, experiments and models.- Observables algebras for solid state systems.- K-theory for topological solid…

A four-dimensional generalization of the quantum Hall effect.

A generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field, is constructed, which has a macroscopic number of degenerate single particle states and forms an incompressible quantum liquid.

Topology and H-flux of T-dual manifolds.

A general formula for the topology and H-flux of the T-dual of a type II compactification is presented, finding that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of theDual H- flux over the dual circle.

Bulk-Edge Correspondence for Two-Dimensional Topological Insulators

Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle…
...