Lecture abstract

Time:   29. September 2020
Place:   Workshop on Quantum Fields and Nonlinear Phenomena, Craiova
Title:   Quantum gravity and elementary particles from higher gauge theory
Abstract:
The 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 2-groups, 3-groups and 4-groups are designed to extend the notions of connection and parallel transport across higher dimensional manifolds. They generalize the concept of gauge symmetry, giving rise to a class of topological actions called 2BF, 3BF and 4BF actions.

We can employ these topological actions by adding appropriate simplicity constraints, in order to describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl and Majorana fields coupled to Einstein-Cartan gravity. It is straightforward to rewrite the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split into a topological sector and simplicity constraints is adapted to the spinfoam quantization techniques, giving rise to a full model of quantum gravity with matter.

In addition, the properties of the gauge n-group structure opens up a possibility of a nontrivial unification of all fields. An n-group naturally contains 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 possibly explain fermion families, and other structure in the matter spectrum of the theory.

Based on arXiv:1110.4694, arXiv:1904.07566 and arXiv:2008.06354.