Related papers: T-duality simplifies bulk-boundary correspondence
We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant…
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has…
Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have…
Advances in material technology and confluence of ideas from particle physics, quantum field theory and condensed matter physics have led to the discovery of new states of matter as well as new physical phenomena: one of them termed as…
We investigate the three-dimensional, time-reversal invariant topological superconductors with generic interaction by their response to external fields. The first description is a gravitational topological field theory, which gives a $Z_2$…
It is known that the topological T-duality exchanges $H$ and $F$-fluxes. In this paper, we reformulate the topological T-duality as an exchange of two Lie algebroids in the generalized tangent bundle. Then, we apply the same formulation to…
We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path…
We study the transport properties of topological insulators, encoding them in a generating functional of gauge and gravitational sources. Much of our focus is on the simple example of a free massive Dirac fermion, the so-called Chern…
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant…
We study the coherent non-equilibrium dynamics of interacting two-dimensional systems after a quench from a trivial to a topological Chern insulator phase. While the many-body wavefunction is constrained to remain topologically trivial…
In previous work on the quantum Hall effect on an annulus, we used $O(d,d;{\bf Z})$ duality transformations on the action describing edge excitations to generate the Haldane hierarchy of Hall conductivities. Here we generate the…
I analyze the properties of thin shells through which the scalar curvature R is discontinuous in gravity theories with R + R^2 Lagrangian on the bulk. These shells/domain walls are of a new kind because they possess, in addition to the…
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlations effects in the two-dimensional case, with a focus on systems with…
In this paper we show that the T-duality transform of Bouwknegt, Evslin and Mathai applies to determine isomorphisms of certain current algebras and their associated vertex algebras on topologically distinct T-dual spacetimes compactified…
In contemporary physics, especially in condensed matter physics, fermionic topological order and its protected edge modes are one of the most important objects. In this work, we propose a systematic construction of the cylinder partition…
Integer and fractional Chern insulators exhibit a nonzero quantized anomalous Hall conductivity due to a spontaneous breaking of time reversal symmetry. To identify nontrivial topology in their time-reversal symmetric many-body spectra, we…
We investigate topological states of two-dimensional (2D) triangular lattices with multi-orbitals. Tight-binding model calculations of a 2D triangular lattice based on $\emph{p}_{x}$ and \emph{p}_{y} orbitals exhibit very interesting doubly…
Time-reversal-invariant topological superconductors have a full paring gap in the bulk and gapless Majorana states at the edge or on the surface. Here, we theoretically propose topological superconductivity in a doped quantum spin Hall…
Fascinating phenomena have been known to arise from the Dirac theory of relativistic quantum mechanics, which describes high energy particles having linear dispersion relations. Electrons in solids usually have non-relativistic dispersion…
Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter…