Casimir scaling and string breaking inG2gluodynamics

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 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 G 2 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 0 , 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.

Phase diagram of the latticeG2Higgs model

“…The same happens for two external charges in the adjoint representation. In a previous work we did observe string breaking at the expected separation between the two charges [13]. The G 2 gauge symmetry can be broken to SU (3) with the help of a Higgs field in the 7 dimensional representation.…”

“…III some algorithmic aspects are reviewed. A more detailed presentation can be found in our earlier paper [13]. Sec.…”

“…The algorithm assumes a local interaction and hence applies to all purely bosonic theories. The implementation for the G 2 Higgs model is a mild generalization of the algorithm used in our previous work on G 2 gluodynamics [13]. We use a local hybrid Monte-Carlo (LHMC) algorithm for several good reasons: First there is no low Metropolis acceptance rate even for large hopping parameters.…”

“…Since we developed and used the first implementation for G 2 it may be useful to sketch how it works for this exceptional group. More details can be found in [13]. For G 2 YMH lattice theory the (L)HMC algorithm is based on a fictitious dynamics for the link-variables on the G 2 manifold and the normalized Higgs field on the 6-sphere.…”

“…In this context confinement refers to confinement at intermediate scales, where a Casimir scaling of string tensions has been detected in [12]. Although the threshold energy for string breaking in G 2 gauge theory is rather high, string breaking has been seen in 3 dimensional G 2 gluodynamics in [13].…”