Non-Abelian gauged Nambu-Jona-Lasinio models on the lattice

We use Monte Carlo simulation to probe the phase structure of a SU(2) gauge theory containing N _f Dirac fermion flavors transforming in the fundamental representation of the group and interacting through an additional four-fermion term. Pairs of physical flavors are implemented using the two tastes present in a reduced staggered fermion formulation of the theory. The resultant lattice theory is invariant under a set of shift symmetries which correspond to a discrete subgroup of the continuum chiral-flavor symmetry. The pseudoreal character of the representation guarantees that the theory has no sign problem. For the case of N _f=4 we observe a crossover in the behavior of the chiral condensate for strong four-fermi coupling associated with the generation of a dynamical mass for the fermions. At weak gauge coupling this crossover is consistent with the usual continuous phase transition seen in the pure (ungauged) Nambu-Jona-Lasinio model. However, if the gauge coupling is strong enough to cause confinement, we observe a much more rapid crossover in the chiral condensate consistent with a first order phase transition.