A spin foam model for pure gauge theory coupled to quantum gravity

TL;DR

This paper introduces a spin foam model that couples pure gauge fields with Riemannian quantum gravity in four dimensions, using a combinatorial triangulation to unify the gravity and gauge sectors.

Contribution

It presents a novel spin foam framework integrating gauge fields with quantum gravity on a combinatorial triangulation, enabling continuum approximation of gauge theory.

Findings

Provides a model combining gauge fields with quantum gravity.

Achieves a continuum limit similar to lattice gauge theory.

Dynamically assigns geometric data to triangulations.

Abstract

We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a four-manifold which is given merely combinatorially. The Riemannian Barrett--Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang--Mills action. The model is designed so that one obtains a continuum approximation of the gauge theory sector at an effective level, similarly to the continuum limit of lattice gauge theory, when the typical length scale of gravity is much smaller than the Yang--Mills scale.