ON LATTICE CHIRAL GAUGE-THEORIES

We consider the Smit-Swift-Aoki formulation of a lattice chiral gauge theory, in which the Wilson and other non-invariant terms in the action are made gauge-invariant by the coupling with a non-linear auxiliary scalar field, OMEGA. We show that OMEGA-decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, barring unforeseen cancellations, explicit ghost fields are necessary to ensure decoupling. Thus, for these theories to give rise to the correct continuum limit, the requirements discussed in our previous work have to be satisfied. Similar considerations apply to schemes with mirror fermions. Finally, we discuss simpler cases with a global chiral symmetry and show that the theory becomes free at decoupling. Recent numerical simulations agree with our considerations.