Casimir scaling and string breaking in G2 gluodynamics

We study the potential energy between static charges in G₂ gluodynamics in three and four dimensions. Our work is based on an efficient local hybrid Monte Carlo algorithm and a multilevel 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 G₂ representations scale with the second order Casimir. In three dimensions Casimir scaling is confirmed within 4% for charges in representations of dimensions 7, 14, 27, 64, 77, 77^', 182, and 189 and in four dimensions within 5% for charges in representations 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. Close to the string breaking distance Casimir scaling between adjoint and defining representation is violated by 2.5%. The analytical prediction for the continuum string tension is confirmed for the defining representation in three dimensions.