210326 Liana David

I will begin with a brief account on the theory of generalized connections and Dirac generating operators on transitive Courant algebroids. I will develop a T-duality for transitive Courant algebroids, which is a generalization of the T-duality of Cavalcanti and Gualtieri in the exact case. I will show that T-duality between transitive Courant agebroids E ra M and tilde{E} ra tilde{M} induces a map between the spaces of sections of the corresponding canonical weighted spinor bundles of E and tilde{E} which intertwines the canonical Dirac generating operators. I will present a general existence result for T-duals under assumptions generalizing the cohomology integrality conditions for the T-duality in the exact case.

If time allows, I will explain that the T-dual of a heterotic Courant algebroid is again heterotic. This is joint work with Vicente Cortes.