Spin Foam Models of Yang-Mills Theory Coupled to Gravity

TL;DR

This paper develops a spin foam model integrating Yang-Mills theory with gravity, using discretized BF theory and Barrett-Crane ansatz, extending from Euclidean to Lorentzian signatures.

Contribution

It introduces a novel spin foam framework for Yang-Mills coupled to gravity, utilizing polynomial interactions and vertex operators on spin networks.

Findings

Derived vertex amplitude for Euclidean gravity case

Extended the model to Lorentzian gravity

Proposed a consistent spin foam model for coupled Yang-Mills and gravity

Abstract

We construct a spin foam model of Yang-Mills theory coupled to gravity by using a discretized path integral of the BF theory with polynomial interactions and the Barret-Crane ansatz. In the Euclidian gravity case we obtain a vertex amplitude which is determined by a vertex operator acting on a simple spin network function. The Euclidian gravity results can be straightforwardly extended to the Lorentzian case, so that we propose a Lorentzian spin foam model of Yang-Mills theory coupled to gravity.