Chiral fermions in two dimensions?

Quenched studies of a global U(1) symmetric Wilson-Yukawa model in two dimensions show no evidence of a charged fermion in the vortex phase at strong Wilson-Yukawa coupling while there is strong indication of a massive neutral fermion. However, with the U(1)$_L$ gauge field turned on, we use dimensional arguments to suggest that the neutral fermion appears to couple chirally to a massive vector boson state.