Integration of Coupling Dirac Structures

TL;DR

This paper explores the integration of coupling Dirac structures, generalizing Hamiltonian fibrations by replacing symplectic structures with Poisson structures, and investigates the associated Poisson gauge theory and integrability obstructions.

Contribution

It provides a detailed study of the integration process for coupling Dirac structures, including explicit geometric descriptions and identification of obstructions to integrability.

Findings

Identified obstructions to the integrability of coupling Dirac structures.

Provided explicit geometric descriptions of the presymplectic groupoid integration.

Extended the understanding of Poisson gauge theory in the context of Dirac structures.

Abstract

Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure. We study the associated Poisson gauge theory, in order to describe the presymplectic groupoid integrating coupling Dirac structures. We find the obstructions to integrability and we give explicit geometric descriptions of the integration.