Generalized Kahler Geometry and the Pluriclosed Flow

In prior work the authors introduced a parabolic flow for pluriclosed metrics, referred to as pluriclosed flow. We also demonstrated that this flow, after certain gauge transformations, gives a class of solutions to the renormalization group flow of the nonlinear sigma model with B-field. Using these transformations, we show that our pluriclosed flow preserves generalized Kahler structures in a natural way. Equivalently, when coupled with a nontrivial evolution equation for the two complex structures, the B-field renormalization group flow also preserves generalized Kahler structure. We emphasize that it is crucial to evolve the complex structures in the right way to establish this fact.Comment: Final version, to appear in Nuc. Phys.

Pluriclosed flow on manifolds with globally generated bundles

We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated