Static Quark Potentials in Quantum Gravity

TL;DR

This paper investigates the potential between static charges in a quantum gravity setting coupled with an SU(2) gauge field, using lattice simulations to analyze confinement and screening behaviors.

Contribution

It introduces a lattice simulation approach to study static quark potentials within quantum gravity coupled to gauge fields, comparing flat and fluctuating geometries.

Findings

Confined phase exhibits linear potential behavior.

Deconfined phase shows screened Coulomb potential.

Quantum gravity effects do not eliminate confinement.

Abstract

We present potentials between static charges from simulations of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. The action consists of the gravitational term given by Regge's discrete version of the Euclidean Einstein action and a gauge term given by the Wilson action, with coupling constants $m_{p}^{2}$ and $\beta$ respectively. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. We compare potentials on a flat simplicial lattice with those on a fluctuating Regge skeleton. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.