Generalized forms of types N = 1, 2 and higher gauge theory

TL;DR

This paper introduces a unified framework for higher gauge theories using generalized forms, enabling a comprehensive description of higher connections, curvatures, gauge transformations, and deriving related action functionals.

Contribution

It develops a formalism for higher gauge theories with generalized forms of types N=1,2, including higher Maurer--Cartan equations and action functionals for Chern--Simons and Yang--Mills theories.

Findings

Unified higher gauge theory formulation using generalized forms.

Derived higher Chern--Simons and Yang--Mills action functionals.

Provided a complete description of higher gauge structures.

Abstract

We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and groups, including the associated higher Maurer--Cartan forms and equations. Using generalized forms of types N = 1, 2, we then provide a complete description of higher gauge structures. Finally, we derive the action functionals for higher Chern--Simons and Yang--Mills theories as applications of the formalism.