A lattice chiral theory with multifermion couplings

Analyzing an SUL(2) ⊗ UR(1) chiral theory with multifermion couplings on a lattice, we find a possible region in the phase space of multifermion couplings, where no spontaneous symmetry breaking occurs, doublers are decoupled as massive Dirac fermions consistently with the SUL(2) ⊗ UR(1) chiral symmetry, the “spectator” fermion ψR(x) is free mode, whereas the normal mode of ψLi(x) is plausibly speculated to be chiral in the continuum limit. This is not in agreement with the general belief of the definite failure of theories so constructed.