Coisotropic branes in symplectic manifolds

TL;DR

This paper studies coisotropic branes in symplectic manifolds, providing explicit descriptions of nearby branes, analyzing their deformations, and exploring conditions for their existence.

Contribution

It offers an explicit description of nearby coisotropic branes and characterizes their infinitesimal deformations using a cochain complex, advancing understanding of brane moduli.

Findings

Explicit description of nearby branes

Cohomological framework for deformations

Conditions for existence of brane structures

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.