Time: 4. July 2022
Place: Symmetries in Quantum Physics 2022, Faro, Portugal
Title: Symmetry in quantum gravity via n-groups
Higher category theory can be employed to generalize the BF action to the so-called nBF action, by passing from the notion of a gauge group to the notion of a gauge n-group. The novel algebraic structures called n-groups are designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus they generalize the concept of gauge symmetry, giving rise to a class of topological actions called nBF actions.
Similarly as for the Plebanski action, one can add appropriate simplicity constraints to topological nBF actions, in order to describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl and Majorana fields coupled to Einstein-Cartan gravity. Specifically, one can rewrite the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split of the full action into a topological sector and simplicity constraints sector is adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter.
In addition, the properties of the gauge n-group structures open up a possibility of a nontrivial unification of all fields. An n-group naturally contains additional novel gauge groups which specify 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. The presence and the properties of these new gauge groups has the potential to explain fermion families, and other structure in the matter spectrum of the theory.
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