Anomalous gauge theories revisited

A possible formulation of chiral gauge theories with an anomalous fermioncontent is re-examined in light of the lattice framework based on theGinsparg-Wilson relation. It is shown that the fermion sector of a wide classof anomalous non-abelian theories cannot consistently be formulated within thislattice framework. In particular, in 4 dimension, {\it all} anomalousnon-abelian theories are included in this class. Anomalous abelian chiral gaugetheories cannot be formulated with compact $\U(1)$ link variables, while anon-compact formulation is possible at least for the vacuum sector in the spaceof lattice gauge fields. Our conclusion is not applied to effective low-energytheories with an anomalous fermion content which are obtained from anunderlying anomaly-free theory by sending the mass of some of fermions toinfinity. For theories with an anomalous fermion content in which the anomalyis cancelled by the Green-Schwarz mechanism, a possibility of a consistentlattice formulation is not clear.Comment: 1+17 pages, uses JHEP3.cls, the final version to appear in JHEP, a note adde