Higher descent equations based on 2-term $L_{\infty}$ algebras

TL;DR

This paper develops higher descent equations for higher gauge theories using 2-term L-infinity algebras, constructing higher Chern-Simons characteristic classes that satisfy these equations.

Contribution

It introduces a framework for higher descent equations in higher gauge theories based on 2-term L-infinity algebras, linking Chern-Weil theory and gauge anomalies.

Findings

Constructed higher Chern-Simons characteristic classes.

Verified these classes satisfy higher descent equations.

Linked higher polynomials to gauge anomalies.

Abstract

In this paper, we develop the higher descent equations for higher gauge theories within the framework of 2-term $L_{\infty}$ algebras. Starting from a multilinear symmetric invariant polynomial, we construct a family of higher Chern-Simons type characteristic classes and verify that they satisfy the higher descent equations. These polynomials encode both the higher Chern-Weil theorem and the higher gauge anomalies.