Casimir Scaling and String Breaking in G(2) Gluodynamics

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 Lüscher-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.

20 pages, 17 figures

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• Glueballs and the Yang-Mills plasma in a $T$-matrix approach
• Topological aspects of G2 Yang-Mills theory
• Quark Confinement in Restricted SU(2) Gauge Theory
• Confinement, Casimir scaling and phase transitions in G(2) gauge theories