Standard Model and 4-groups

Abstract

We show that a categorical generalization of the the Poincaré symmetry which is based on the n-crossed modules becomes natural and simple when n=3 and that the corresponding 3-form and 4-form gauge fields have to be a Dirac spinor and a Lorentz scalar, respectively. Hence by using a Poincaré 4-group we naturally incorporate fermionic and scalar matter into the corresponding 4-connection. The internal symmetries can be included into the 4-group structure by using a 3-crossed module based on the $SL(2,\mathbb{C})\times K$ group, so that for $K=U(1)\times SU(2)\times SU(3)$ we can include the Standard Model into this categorification scheme.

v2: published version, 4 pages

References in corpus (1)

• Canonical formulation of Poincare BFCG theory and its quantization

Cited by in corpus (8)

• Topological invariant of 4-manifolds based on a 3-group
• 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
• 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
• The 3BF theory as a TQFT
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity