Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity

Abstract

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.

v3: published version, 31 pages

References in corpus (15)

• Higher-form symmetries and 3-group in axion electrodynamics
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• $BF$ gravity
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Topological Higher Gauge Theory - from BF to BFCG theory
• Semistrict Higher Gauge Theory
• Parent formulation at the Lagrangian level
• Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
• Canonical formulation of Poincare BFCG theory and its quantization
• Standard Model and 4-groups
• 3-form Yang-Mills based on 2-crossed modules
• Gauge symmetry of the 3BF theory for a generic Lie 3-group
• Higher form Yang-Mills as higher BFYM theories
• Gravity with torsion as deformed $BF$ theory
• Henneaux-Teitelboim gauge symmetry and its applications to higher gauge theories

Cited by in corpus (2)

• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• The 3BF theory as a TQFT