Non-abelian Gerbes and Enhanced Leibniz Algebras

TL;DR

This paper develops a general gauge-invariant action for coupled 1- and 2-form gauge fields, revealing how gauge invariance constrains the algebraic structure to an enhanced Leibniz algebra, advancing higher gauge theory formulations.

Contribution

It introduces the most general gauge-invariant action for 1- and 2-form gauge fields and links semi-strict Lie 2-algebras to enhanced Leibniz algebras, aiding higher gauge theories.

Findings

Derived a general gauge-invariant action functional.

Showed reduction of Lie 2-algebra to enhanced Leibniz algebra.

Connected gauge invariance to algebraic structure constraints.

Abstract

We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge invariant functional enforces that the most general semi-strict Lie 2-algebra describing the bundle of a non-abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p, solved here for p = 2.