Casimir Scaling and String Breaking in G(2) Gluodynamics

TL;DR

This study investigates the potential energy and string tension scaling in G(2) gluodynamics across three and four dimensions, confirming Casimir scaling at intermediate scales and observing string breaking phenomena.

Contribution

It provides the first detailed numerical confirmation of Casimir scaling and string breaking in G(2) gauge theory using advanced Monte Carlo algorithms.

Findings

Casimir scaling confirmed within 1-5% for various representations

String breaking observed in three dimensions for fundamental charges

String tension scales with the second order Casimir at intermediate distances

Abstract

We study the potential energy between static charges in G(2) gluodynamics in three and four dimensions. Our work is based on an efficient local hybrid Monte-Carlo algorithm and a multi-level L\"uscher-Weisz algorithm with exponential error reduction to accurately measure expectation values of Wilson- and Polyakov loops. Both in three and four dimensions we show that at intermediate scales the string tensions for charges in various G(2)-representations scale with the second order Casimir. In three dimensions Casimir scaling is confirmed within one percent for charges in representations of dimensions 7, 14, 27, 64, 77, 77', 182 and 189 and in 4 dimensions within 5 percent for charges in representions of dimensions 7, 14, 27 and 64. In three dimensions we detect string breaking for charges in the two fundamental representations. The scale for string breaking agrees very well with the mass of the created pair of glue-lumps.