NON-GAUGE FIXING APPROACH TO CHIRAL GAUGE-THEORIES USING STAGGERED FERMIONS

We investigate a proposal for the construction of models with chiral f ermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions t o the gauge fields. Motivated by previous results in the gauge non-inv ariant massive Yang-Mills theory and certain gauge-fermion models we a im at a dynamical restoration of the gauge invariance in the full quan tum model. If the gauge symmetry breaking is not too severe, this proc edure could lead in the continuum limit to the desired gauge invarian chiral gauge theory. This scenario is very attractive since it does no t rely on gauge fixing. We investigate a simple realization of this ap proach in a U(1) axial-vector model with dynamical fermions in four di mensions. A detailed numerical exploration of the phase diagram of thi s model on small lattices gives us no indication that the desired gaug e symmetry restoration takes place. Since simulation of the model on l arger lattices leads to severe numerical problems, we conclude that th is simple realization of the non-gauge fixing approach has failed, at least in practice.