Related papers: T-duality of current algebras and their quantizati…
We introduce the notion of crystallographic T-duality, inspired by the appearance of $K$-theory with graded equivariant twists in the study of topological crystalline materials. Besides giving a range of new topological T-dualities, it also…
We extend the T-duality for gauge theory to that on curved space described as a nontrivial fiber bundle. We also present a new viewpoint concerning the consistent truncation and the T-duality for gauge theory and discuss the relation…
We construct a topological sigma model and a current algebra based on a Courant algebroid structure on a Poisson manifold. In order to construct models, we reformulate the Poisson Courant algebroid by supergeometric construction on a…
A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…
T-duality (Fourier-Mukai duality) and properties of classical instanton moduli spaces can be used to deduce some properties of $\alpha^{\prime}$-corrected moduli spaces of branes for Type IIA string theory compactified on $K3$ or $T^4$.…
We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus.…
In this paper, we establish graded T-duality for $2d$ $\sigma$-models with $H$-flux after localization. This establishes the most general version of T-duality for Type II String Theory. The graded T-duality map, which we call {\bf graded…
We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…
This paper is a step towards realizing T-duality and Hori formulae for loop spaces. Here we prove T-duality and Hori formulae for winding q-loop spaces, which are infinite dimensional subspaces of loop spaces.
We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged…
We develop a theory of T-duality for transitive Courant algebroids. We show that T-duality between transitive Courant algebroids E\rightarrow M and \tilde{E}\rightarrow \tilde{M} induces a map between the spaces of sections of the…
Recently we initiated the study of spherical T-duality for spacetimes that are principal SU(2)-bundles. In this paper, we extend spherical T-duality to spacetimes that are oriented non-principal SU(2)-bundles. There are several interesting…
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 affirmative several earlier conjectures of…
This submission is a PhD dissertation. Kapustin and Witten conjectured that there is a mirror symmetry relation between the hyperk\"ahler structures on certain Higgs bundle moduli spaces. As a consequence, they conjecture an equivalence…
We give a systematic derivation of the local expressions of the NS H-flux, geometric F- as well as non-geometric Q- and R-fluxes in terms of bivector beta- and two-form B-potentials including vielbeins. They are obtained using a…
We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified…
We revisit T-duality transformations for the open string via Buscher's procedure and work-out technical details which have been missing so far in the literature. We take into account non-trivial topologies of the world-sheet, we consider…
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled…
A "reduced" differential geometry adapted to the presence of abelian isometries is constructed.Classical T-duality diagonalizes in this setting, allowing us to get conveniently the transformation of the relevant geometrical objects such as…
Darboux theorem in symplectic geometry is the crux of emergent gravity in which the gravitational metric emerges from a noncommutative U(1)-theory. Topological T-duality, on the other hand, is a relation between two a priori different…