The Standard Model and the Lattice

TL;DR

This paper demonstrates how the Standard Model's gauge structure can be represented on a lattice, capturing key features like parity violation and anomalies, thus bridging continuum theory and lattice formulations.

Contribution

It introduces a lattice gauge formulation of the Standard Model that incorporates parity violation and anomalies using the pseudo-reality of the weak group.

Findings

Successfully maps Standard Model onto lattice with parity violation

Shows anomalies are represented via Dirac eigenstates

Addresses gauge configuration effects on zero modes

Abstract

The $SU(3)\otimes SU(2) \otimes U(1)$ standard model maps smoothly onto a conventional lattice gauge formulation, including the parity violation of the weak interactions. The formulation makes use of the pseudo-reality of the weak group and requires the inclusion a full generation of both leptons and quarks. As in continuum discussions, chiral eigenstates of the Dirac operator generate known anomalies, although with rough gauge configurations these are no longer exact zero modes of the Dirac operator.