Four fermion interactions in non-Abelian gauge theory

Abstract

We continue our earlier study of the phase structure of a $SU(2)$ gauge theory whose action contains additional chirally invariant four fermion interactions. Our lattice theory uses a reduced staggered fermion formalism to generate two Dirac flavors in the continuum limit. In the current study we have tried to reduce lattice spacing and taste breaking effects by using an improved fermion action incorporating stout smeared links. As in our earlier study we observe two regimes; for weak gauge coupling the chiral condensate behaves as an order parameter differentiating a phase at small four Fermi coupling where the condensate vanishes from a phase at strong four Fermi coupling in which chiral symmetry is spontaneously broken. This picture changes qualitatively when the gauge coupling is strong enough to cause confinement; in this case we observe a phase transition for some critical value of the four Fermi coupling associated with a strong enhancement of the chiral condensate. We present evidence that this transition is likely first order. Furthermore, we observe that the critical four Fermi coupling varies monotonically with bare gauge coupling---decreasing, as expected, as the gauge coupling is increased. We have checked that these results remain stable under differing levels of smearing. These results argue against the appearance of new fixed points associated with chirally invariant four fermion interactions in confining non-Abelian gauge theories.