A Possible Lattice Chiral Gauge Theory

Abstract

We analyze the dynamics of an $S{U}_L(2)\otimes U_R(1)$ chiral gauge theory on a lattice with a large multifermion coupling $1\ll g_2<\infty$. It is shown that no spontaneous symmetry breaking occurs; the ``spectator'' fermion ${\psi }_R(x)$ is a free mode; doublers are decoupled as massive Dirac fermions consistently with the chiral gauge symmetry. Whether right-handed three-fermion states disappear and chiral fermions emerge in the low-energy limit are discussed. Provided right-handed three-fermion states disappear, we discuss the chiral gauge coupling, Ward identities, the gauge anomaly and anomalous $U_L(1)$ global current within the gauge-invariant prescription of renormalization of the gauge perturbation theory.

Comments: 26 pages, Latex, sections 1 and 5 are revised