ON LATTICE DEFINITIONS OF CHIRAL GAUGE-THEORIES AND THE PROBLEM OF ANOMALIES

We argue that many lattice formulations of chiral gauge theories cannot reproduce the continuum theories that they are supposed to define. The lattice models contain global symmetries that are broken by anomalies in the continuum. To the extent that the lattice theories reproduce the low lying spectrum of the continuum models. the effective action they generate must contain Wess-Zumino terms that cancel these anomalies. In particular, many otherwise appealing lattice formulations of the standard model cannot reproduce the baryon number violating phenomena that have been the focus of much recent interest.