We investigate gauge theories based on the smallest exceptional simple lie group G 2 . Our first model considered here is G 2 Yang-Mills coupled to a fundamental Higgs field. In 4 spacetime dimensions we explore the phase diagram of the theory, showing that at larger Higgs masses the first order deconfinement phase transition turns into a crossover and therefore connects the low temperature confined phase with the high temperature deconfined phase. The second model investigated is G 2 Yang-Mills coupled to fundamental fermions. It shares many features with QCD, especially fermionic baryons, but due to the absence of the fermion sign problem we can investigate this theory with Monte Carlo techniques even at low temperature and high baryonic density. First results on small lattices are presented.

Due to the fermion sign problem, standard lattice Monte-Carlo method for QCD fail at small temperatures and high baryon densities. G 2 -QCD, QCD with the gauge group SU(3) replaced by the exceptional Lie group G 2 , can be simulated using lattice techniques at these densities, and can therefore provide an illustration of the possible phase structure. Here we present a systematic investigation of the ground-state hadronic spectrum using lattice simulations for different quark masses in several hadronic sectors. We then show that the different hadronic scales of Goldstone bosons, intermediate bosons, and baryons is reflected in the phase structure at finite density.

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 Lüscher-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.