Extended Cartan homotopy formula for higher Chern-Simons-Antoniadis-Savvidy theory

TL;DR

This paper develops an extended Cartan homotopy formula for higher gauge theories, demonstrating its role in deriving higher Chern-Weil theorems, triangle equations, and transgression forms in the context of higher Chern-Simons theories.

Contribution

It introduces a higher-dimensional Cartan homotopy formula and applies it to higher Chern-Simons theories, establishing new geometric relations and forms.

Findings

Derived higher Chern-Weil theorem using ECHF

Established higher triangle equation in gauge theory

Expressed higher transgression form as a difference of higher ChSAS forms

Abstract

We consider extended Cartan homotopy formula (ECHF) for higher gauge theory. Firstly, we construct an oriented simplex based on 2-connections and present differential and integral forms of the higher ECHF. Then, we study the higher Chern-Simons-Antoniadis-Savvidy (ChSAS) theory and prove that the higher ECHF can reproduce the higher Chern-Weil theorem and give higher triangle equation. We finally conclude from the higher ECHF that a higher transgression form can be written as the difference of two higher ChSAS forms minus an exact form.