Reduction of branes in generalized complex geometry

Zambon, M (2008). Reduction of branes in generalized complex geometry. Journal of Symplectic Geometry, 6(4):353-378.

Abstract

We show that certain submanifolds of generalized complex manifolds (“weak branes”) admit a natural quotient which inherits a generalized complex structure. This is analog to quotienting coisotropic submanifolds of symplectic manifolds. In particular, Gualtieri’s generalized complex submanifolds (“branes”) quotient to space-filling branes. Along the way, we perform reductions by foliations (i.e., no group action is involved) for exact Courant algebroids—interpreting the reduced ˇSevera class—and for Dirac structures.

Abstract

We show that certain submanifolds of generalized complex manifolds (“weak branes”) admit a natural quotient which inherits a generalized complex structure. This is analog to quotienting coisotropic submanifolds of symplectic manifolds. In particular, Gualtieri’s generalized complex submanifolds (“branes”) quotient to space-filling branes. Along the way, we perform reductions by foliations (i.e., no group action is involved) for exact Courant algebroids—interpreting the reduced ˇSevera class—and for Dirac structures.

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