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

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.