On the infinitesimal Gauge Symmetries of closed forms

TL;DR

This paper explores the geometric structure of closed differential forms on fibrations, introducing 2-plectic fibrations and higher connection analogues to model abstract field theories related to symplectic and Yang-Mills theories.

Contribution

It introduces the concept of 2-plectic fibrations and interprets the equations for coupling as higher analogues of connections, advancing the geometric understanding of field theories.

Findings

Defined 2-plectic fibrations as a new geometric structure.

Provided a geometric interpretation of coupling equations in higher forms.

Linked symplectic fibrations to classical Yang-Mills theories.

Abstract

Motivated by the relationship between symplectic fibrations and classical Yang-Mills theories, we study the closeness of a $n$-form (n=2,3) defined on the total space of a fibration as a simple model for an abstract field theory. We introduce 2-plectic fibrations and interpret geometrically the corresponding equations for coupling in terms of higher analogues of connections.