3-form Yang-Mills based on 2-crossed modules

Abstract

In this paper, we study the higher Yang-Mills theory in the framework of higher gauge theory. It was shown that the 2-form electromagnetism can be generalized to the 2-form Yang-Mills theory with the group $U(1)$ replaced by a crossed module of Lie groups. To extend this theory to even higher structure, we develop a 3-form Yang-Mills theory with a 2-crossed module of Lie groups. First, we give an explicit construction of non-degenerate symmetric $G$-invariant forms on the 2-crossed module of Lie algebras. Then, we derive the 3-Bianchi-Identities for 3-curvatures. Finally, we create a 3-form Yang-Mills action and obtain the corresponding field equations.

arXiv comment16 pages

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Cited by in corpus (5)

• Topological invariant of 4-manifolds based on a 3-group
• Higher Chern-Simons based on (2-)crossed modules
• Henneaux-Teitelboim gauge symmetry and its applications to higher gauge theories
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity