Generalized Kahler Geometry and the Pluriclosed Flow

TL;DR

This paper studies a geometric flow called pluriclosed flow, showing it preserves generalized Kahler structures and connects to the B-field renormalization group flow, with implications for complex geometry and theoretical physics.

Contribution

It demonstrates that pluriclosed flow preserves generalized Kahler structures when coupled with appropriate evolution of complex structures.

Findings

Pluriclosed flow preserves generalized Kahler structures.

Coupled flow with complex structures aligns with B-field renormalization group flow.

Proper evolution of complex structures is crucial for preservation.

Abstract

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.