Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory on the lattice

Abstract

We consider the cohomological classification of the 4+2-dimensional topological field, which is proposed by Lüscher, for SU(2)_L \times U(1)_Y electroweak theory. The dependence on the admissible abelian gauge field of U(1)_Y is determined through topological argument, with 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 \times U(1)_Y at finite lattice spacing, as well as {U(1)_Y}^3, using the pseudo reality of SU(2)_L and the anomaly cancellation conditions in the electroweak theory given in terms of the hyper-charges of U(1)_Y.

Comments: 23 pages, 1 figure, LaTeX2e, minor corrections, references added