Confinement, Casimir scaling and phase transitions in G(2) gauge theories

TL;DR

This paper introduces advanced algorithms to study G(2) gauge theories, revealing Casimir scaling, string breaking, and phase transition behaviors in three and four dimensions, enhancing understanding of confinement mechanisms.

Contribution

It develops efficient Monte Carlo algorithms and applies them to analyze G(2) gauge theories, uncovering detailed confinement and phase transition phenomena.

Findings

Casimir scaling observed at intermediate scales in G(2) representations

String breaking occurs at predicted scales for fundamental charges

Phase diagram shows confinement-deconfinement transitions connecting G(2) and SU(3)

Abstract

We present an efficient local hybrid Monte-Carlo algorithm to investigate G(2) gluodynamics with and without Higgs field in 3 and 4 dimensions. Additionaly we implemented a modified version of the multi-level L\"uscher-Weisz algorithm with exponential error reduction to measure expectation values of Wilson and Polyakov loops. In three dimensions we show that at intermediate scales the potential between static charges in the eight lowest-dimensional representations of G(2) scale with the eigenvalues of the quadratic Casimir operator. For the fundamental representations we detect string breaking for larger separations of the charges at precisely the scale predicted by the mass of the created pair of glue-lumps. In four dimensions we explored the phase diagram of the G(2) Gauge Higgs model showing that a line of first order confinement-deconfinement phase transitions connects G(2) and SU(3) gluodynamics and a line of second order phase transitions separates the two deconfinement phases.