Gauge anomaly cancellations in SU(2)(L) x U(1)(Y) electroweak theory on the lattice

We consider the cohomological classification of the (4 + 2)-dimensional top ological field which was proposed by Luscher, for the SU(2)(L) x U(1)(Y) el ectroweak theory. The dependence on the admissible abelian gauge field of U (1)(Y) is determined through topological argument, with the SU(2)(L) gauge field fixed as background. We then show the exact cancellation of the local gauge anomaly of the mixed type SU(2)(L)(2) x U(1)(Y) at a finite lattice spacing, as well as U(1)(Y)(3), using the pseudo reality of SU(2)(L) and th e anomaly cancellation conditions in the electroweak theory given in terms of the hyper-charges of U(1)(Y), (C) 2001 Elsevier Science B.V. All rights reserved.