Generalized higher connections and Yang-Mills

TL;DR

This paper extends differential calculus to higher structures, develops generalized higher connections, and formulates corresponding Yang-Mills theories, advancing the mathematical framework for gauge theories in higher dimensions.

Contribution

It introduces a generalized differential calculus framework for higher structures and formulates new higher gauge theories with their field equations.

Findings

Derived higher Bianchi identities

Established generalized 2- and 3-form Yang-Mills theories

Analyzed gauge transformations for higher connections

Abstract

We first extend Generalized Differential Calculus (GDC) to higher structures and create generalized G-invariant bilinear forms. In addition, we also focus on developing generalized 2- and 3-connection theories in the framework of GDC. Then, we derive the higher Bianchi-Identities and study the gauge transformations for those generalized higher connections. Finally, we establish the generalized 2- and 3-form Yang-Mills theories based on GDC and obtain the corresponding fields equations.