D-branes, T-duality, and index theory

D-Branes, T-Duality, and Index Theory

We show that the transformation of D-branes under T-duality on fourtorus is represented by Nahm transform of instantons. The argument for this allows us to generalize Nahm transform to the case of orthogonal and symplectic gauge groups as well as to instantons on Z2 orbifold of four-torus. In addition, we identify the isomorphism of K-theory groups that realizes the transformation of D-brane ch...

Geometric aspects of D-branes and T-duality

We explore the differential geometry of T-duality and D-branes. Because D-branes and RR-fields are properly described via K-theory, we discuss the (differential) K-theoretic generalization of T-duality and its application to the coupling of D-branes to RR-fields. This leads to a puzzle involving the transformation of the A-roof genera in the coupling.

Statistical Mechanics of Vortices from D-branes and T-duality

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian ...

, Duality and D - Branes in Bivariant K - Theory

We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C∗-algebras. We present a new description of bivariant K-theory in terms of noncommutative correspondences which is nicely adapted to the study of T-duality in open string theory. We systematically use the diagram calculus for bivariant K-theory as detailed...

D - branes in the Euclidean AdS 3 and T - duality