Reduction of branes in generalized complex geometry

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.