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

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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.