Quantum gravity and elementary particles from higher gauge theory

TL;DR

This paper explores coupling general relativity with the Standard Model using higher gauge theory, introducing 3-groups for a unified description suitable for spinfoam quantization, and analyzing matter fields and fermion families.

Contribution

It provides an explicit algebraic construction of the Standard Model coupled to gravity within higher gauge theory, emphasizing the role of 3-groups for gauge symmetry and matter classification.

Findings

Constructed a classical action suitable for spinfoam quantization.

Highlighted the advantages of 3-groups over Lie groups for gauge symmetry.

Discussed the classification of matter fields and fermion families.

Abstract

We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all relevant mathematical concepts, most notably the idea of a categorical ladder, 3-groups and generalized parallel transport. Then, we give an explicit construction of the algebraic structure which describes the full Standard Model coupled to Einstein-Cartan gravity, along with the classical action, written in the form suitable for the spinfoam quantization procedure. We emphasize the usefulness of the 3-group concept as a superior tool to describe gauge symmetry, compared to an ordinary Lie group, as well as the possibility to employ this new structure to classify matter fields and study their spectrum, including the origin of fermion families.