Construction and examples of higher gauge theories
arXiv:2005.09404
Abstract
We provide several examples of higher gauge theories, constructed as generalizations of a BF model to 2BF and 3BF models with constraints. Using the framework of higher category theory, we introduce appropriate 2-groups and 3-groups, and construct the actions for the corresponding constrained 2BF and 3BF theories. In this way, we can construct actions which describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. Each action is naturally split into a topological sector and a sector with simplicity constraints. The properties of the higher gauge group structure opens up a possibility of a nontrivial unification of all fields.
arXiv comment26 pages, contribution to the MPHYS10 2019 conference proceedings
References in corpus (8)
- LQG vertex with finite Immirzi parameter
- Topological Lattice Models in Four Dimensions
- An Invitation to Higher Gauge Theory
- Poincare 2-group and quantum gravity
- 2-categorical Poincare Representations and State Sum Applications
- Spin-cube Models of Quantum Gravity
- Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
- Causal Dynamical Triangulations in the Spincube Model of Quantum Gravity