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A 3BF model of quantum gravity coupled to Standard Model matter

Pavle Stipsic, Marko Vojinovic

Abstract

We develop an explicit model of quantum gravity coupled to the matter fields of the Standard Model, based on the 3-group structure and the 3BF action, within the framework of higher gauge theory. The model is constructed by providing a rigorous definition for the path integral of the theory, achieved by defining the whole theory on a piecewise-flat spacetime manifold. To that end, we develop a method to systematically discretize both the action and the path integral measure by passing from a smooth manifold to a piecewise-flat manifold. Finally, we discuss in some detail the structure of the resulting quantum gravity model, and provide a preliminary analysis of its semiclassical limit.

A 3BF model of quantum gravity coupled to Standard Model matter

Abstract

We develop an explicit model of quantum gravity coupled to the matter fields of the Standard Model, based on the 3-group structure and the 3BF action, within the framework of higher gauge theory. The model is constructed by providing a rigorous definition for the path integral of the theory, achieved by defining the whole theory on a piecewise-flat spacetime manifold. To that end, we develop a method to systematically discretize both the action and the path integral measure by passing from a smooth manifold to a piecewise-flat manifold. Finally, we discuss in some detail the structure of the resulting quantum gravity model, and provide a preliminary analysis of its semiclassical limit.
Paper Structure (24 sections, 169 equations, 3 tables)

This paper contains 24 sections, 169 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Short review of the classical $3BF$ action
  3. The $3$-group and the topological $3BF$ action
  4. The Standard Model $3BF$ action
  5. The Einstein-Cartan contact action
  6. Discretization of the action
  7. Preliminaries
  8. Combinatorial analysis
  9. Discretization of the integral
  10. Discretization of the derivative
  11. Discretization of the path integral
  12. Application to the Standard Model 3BF action
  13. General structure of the model
  14. Yang-Mills kinetic term
  15. Regge action term
  16. ...and 9 more sections