Generalized Kahler Geometry and the Pluriclosed Flow

Details Generalized Kahler Geometry and the Pluriclosed Flow Generalized Kahler Geometry and the Pluriclosed Flow

2011-09-02

arxiv.org/abs/1109.0503v2

Mathematics

Differential Geometry

Final version, to appear in Nuc. Phys. B

Scientific paper

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.

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