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

Phase diagram of the G(2) Higgs model and G(2)-QCD