Generalized Kahler Geometry and the Pluriclosed Flow

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.

Final version, to appear in Nuc. Phys. B

References in corpus (2)

• Generalized Kahler geometry
• Regularity results for pluriclosed flow

Cited by in corpus (22)

• Torsion-free generalized connections and Heterotic Supergravity
• The long-time behavior of the homogeneous pluriclosed flow
• Generalized Kähler almost abelian Lie groups
• The Gibbons-Hawking ansatz in generalized Kähler geometry
• Hermitian Curvature flow on unimodular Lie groups and static invariant metrics
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Infinite families of homogeneous Bismut Ricci flat manifolds
• The Heterotic-Ricci flow and its three-dimensional solitons
• Special Lagrangian cycles and Calabi-Yau transitions
• Expanding solitons to the Hermitian curvature flow on complex Lie groups
• A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed Flow
• CYT and SKT manifolds with parallel Bismut torsion
• Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds
• Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries
• On the dynamical behaviour of the generalized Ricci flow
• The deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds
• Classification of generalized Kähler-Ricci solitons on complex surfaces
• On canonical metrics of complex surfaces with split tangent and related geometric PDEs
• Lie-Algebraic Curvature Conditions preserved by the Hermitian Curvature Flow
• Bismut Ricci flat manifolds with symmetries
• Optimal Transport and Generalized Ricci Flow
• The parabolic split-type Monge-Ampere on split tangent bundle surfaces