Coupling Yang-Mills with Causal Dynamical Triangulations

TL;DR

This paper develops algorithms for coupling Yang-Mills gauge fields to quantum gravity within the Causal Dynamical Triangulations framework and presents simulation results for 2D cases with U(1) and SU(2) gauge groups.

Contribution

It introduces a general algorithm for coupling gauge fields to quantum gravity in CDT and provides simulation results for 2D models with different gauge groups.

Findings

Simulations show how gauge fields influence quantum gravity in 2D.

Comparison with flat case highlights effects of dynamical geometry.

Algorithm applicable to various dimensions and gauge groups.

Abstract

We discuss the algorithmic problem of minimal coupling gauge fields of the Yang-Mills type to Quantum Gravity in the approach known as Causal Dynamical Triangulations (CDT) as a step towards studying, ultimately, systems of gravity coupled with bosonic and fermionic matter. We first describe the algorithm for general dimensions and gauge groups and then focus on the results obtained from simulations of 2d CDT coupled to gauge fields with U{(1)} and SU{(2)} gauge groups, where we studied both observables related to gravity and gauge fields, and compared them with analogous simulations in the static flat case.