A boundary state sum for the 3BF theory is constructed and proved to satisfy Atiyah's axioms, giving a TQFT functor for finite 3-groups on triangulable 4-manifolds.
Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
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We study the details of the explicit and spontaneous symmetry breaking of the constrained 3BF action representing the Standard Model coupled to Einstein-Cartan gravity. First we discuss how each particular constraint breaks the original symmetry of the topological 3BF action. Then we investigate the spontaneous symmetry breaking and the Higgs mechanism for the electroweak theory in the constrained 3BF form, in order to demonstrate that they can indeed be performed in the framework of higher gauge theory. A formulation of the Proca action as a constrained 3BF theory is also studied in detail.
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The 3BF theory as a TQFT
A boundary state sum for the 3BF theory is constructed and proved to satisfy Atiyah's axioms, giving a TQFT functor for finite 3-groups on triangulable 4-manifolds.