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 ψ i L(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. March, 1996 PACS 11.15Ha, 11.30.Rd, 11.30.Qc a) E-mail address: [email protected] 1. It is a long standing problem to regularize chiral gauge theories on a lattice and it seems that none of the methods proposed has been consistently and completely demonstrated both to ensure that an asymptotically chiral gauge theory in the continuum limit really exists and to provide a framework for doing nonperturbative calculation in these theories [1]. It is generally believed that the constructions [2, 3] of chiral gauge theories on the lattice with external multifermion couplings fail to give chiral gauged fermions in the continuum limit for the reason[4] that the theories so constructed undergo spontaneous symmetry breaking and their phase structure is similar to that of the Smit-Swift model[5], which has been very carefully studied and shown to fail. Nevertheless, we believe that further considerations of constructing CGT on a lattice with external multifermion couplings and careful studies of the spectrum in each phase of such a constructed theory are necessary. In fact, we find a possible scaling region of defining continuum chiral fermion in such a formulation of chiral gauge theories on the lattice. Let us consider the following fermion action of the SUL(2) CGT on a lattice with two external multifermion couplings.