Interpreting the lattice monopoles in the continuum terms

TL;DR

This paper reviews how lattice monopoles, identified via Maximal Abelian Projection, relate to continuum theories, highlighting their association with singular fields and critiquing assumptions of regularity in recent analyses.

Contribution

It clarifies the continuum interpretation of lattice monopoles and challenges the assumption of regular fields in recent studies.

Findings

Lattice monopoles are linked to singular fields in the continuum.

Current lattice data suggest monopoles are associated with singularities.

Critique of the assumption that monopole fields are regular.

Abstract

We review briefly current interpretation of the lattice monopoles, defined within the Maximal Abelian Projection, in terms of the continuum theory. We emphasize, in particular, that the lattice data, at the presently available lattices, indicate that the monopoles are associated with singular fields. This note is prompted by a recent analysis hep-lat/0211005 which is based on an implicit assumption that the fields are regular.