Coisotropic branes in symplectic manifolds

Abstract

A brane in a symplectic manifold is a coisotropic submanifold $Y$ endowed with a compatible closed $2$-form $F$, which together induce a transverse complex structure. For a specific class of branes, we give an explicit description of branes nearby a given one, and for arbitrary branes, we describe the infinitesimal deformations and provide an associated cochain complex. As an application, we determine to what extent coisotropic submanifolds near a given brane admit brane structures.