A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance

TL;DR

This paper develops a gauge-invariant, non-perturbative lattice formulation of the Glashow-Weinberg-Salam model using Ginsparg-Wilson fermions, enabling a consistent regularization of the electroweak theory.

Contribution

It introduces a construction of the electroweak model on the lattice with exact gauge invariance, covering all topological sectors and ensuring a smooth fermion measure.

Findings

Provides a gauge-invariant regularization of the electroweak theory to all orders.

Constructs local currents satisfying the reconstruction theorem.

Enables non-perturbative studies of the electroweak sector on the lattice.

Abstract

We present a gauge-invariant and non-perturbative construction of the Glashow-Weinberg-Salam model on the lattice, based on the lattice Dirac operator satisfying the Ginsparg-Wilson relation. Our construction covers all SU(2) topological sectors with vanishing U(1) magnetic flux and would be usable for a description of the baryon number non-conservation. In infinite volume, it provides a gauge-invariant regularization of the electroweak theory to all orders of perturbation theory. First we formulate the reconstruction theorem which asserts that if there exists a set of local currents satisfying cetain properties, it is possible to reconstruct the fermion measure which depends smoothly on the gauge fields and fulfills the fundamental requirements such as locality, gauge-invariance and lattice symmetries. Then we give a closed formula of the local currents required for the reconstruction theorem.