Higher Gauge Theories Based on 3-groups

Abstract

We study the categorical generalizations of a $BF$ theory to $2BF$ and $3BF$ theories, corresponding to $2$-groups and $3$-groups, in the framework of higher gauge theory. In particular, we construct the constrained $3BF$ actions describing the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl and Majorana fields coupled to Einstein-Cartan gravity. The action is naturally split into a topological sector and a sector with simplicity constraints, adapted to the spinfoam quantization programme. In addition, the structure of the $3$-group gives rise to a novel gauge group which specifies the spectrum of matter fields present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. This allows us to rewrite the whole Standard Model coupled to gravity as a constrained $3BF$ action, facilitating the nonperturbative quantization of both gravity and matter fields. Moreover, the presence and the properties of this new gauge group open up a possibility of a nontrivial unification of all fields and a possible explanation of fermion families and all other structure in the matter spectrum of the theory.

arXiv commentv4: published version

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Cited by in corpus (14)

• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Topological invariant of 4-manifolds based on a 3-group
• Standard Model and 4-groups
• (2-)Drinfel'd Double and (2-)BF Theory
• Gauge symmetry of the 3BF theory for a generic Lie 3-group
• Higher form Yang-Mills as higher BFYM theories
• Higher Chern-Simons based on (2-)crossed modules
• Extended Cartan homotopy formula for higher Chern-Simons-Antoniadis-Savvidy theory
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• The 3BF theory as a TQFT
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• Categorical generalization of BF theory coupled to gravity
• Adjusting Higher Chern-Simons Theory
• Heavy-quark mass relation from a standard-model boson operator representation in terms of fermions