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arXiv · 2108.12852

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

Danhua Song·Kai Lou·Ke Wu·Jie Yang·Fuhao Zhang
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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.

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Danhua Song, Kai Lou, Ke Wu, Jie Yang, Fuhao Zhang. 2021-08-29. 3-form Yang-Mills based on 2-crossed modules. https://doi.org/10.1016/j.geomphys.2022.104537

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