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

TL;DR

This paper investigates the topological classification of gauge anomalies in lattice electroweak theory, demonstrating exact cancellation of mixed and pure anomalies at finite lattice spacing through topological and algebraic methods.

Contribution

It provides a cohomological analysis of gauge anomaly cancellations in lattice electroweak theory, explicitly showing anomaly cancellation conditions at finite lattice spacing.

Findings

Exact cancellation of mixed SU(2)_L^2 imes U(1)_Y anomaly.

Exact cancellation of U(1)_Y^3 anomaly.

Topological classification of anomalies on the lattice.

Abstract

We consider the cohomological classification of the 4+2-dimensional topological field, which is proposed by L\"uscher, 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.