Non-abelian Gerbes and Enhanced Leibniz Algebras

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.

Accepted for Publication in Rapid Communications PRD, submitted originally on April 8, final revised version on June 30

References in corpus (4)

• General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroids
• Semistrict Higher Gauge Theory
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• The end of the p-form hierarchy

Cited by in corpus (6)

• Gravitational wave memory beyond general relativity
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• Leibniz-Yang-Mills Gauge Theories and the 2-Higgs Mechanism
• All maximal gauged supergravities with uplift
• Basic curvature and the Atiyah cocycle in gauge theory
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies