Topological Renormalisation of the O(3) Sigma Model

TL;DR

This paper addresses divergences in the O(3) Sigma Model's instanton sector by introducing a topological counter-term, aiming to resolve dependence issues in Green's functions caused by field configuration degeneracies.

Contribution

It proposes a novel topological renormalization method that cancels instanton sector divergences in the O(3) Sigma Model, improving the consistency of Green's function calculations.

Findings

Divergences linked to instanton moduli space are identified.

A topological counter-term is constructed to cancel these divergences.

The approach reduces dependence of Green's functions on field splitting.

Abstract

We show that the one-instanton sector moduli-space divergence of the O(3) Sigma Model leads to an unacceptable dependence of Green's functions on the arbitrary way that the field is split into a quantum fluctuation about a classical background. Since the divergence is associated with the degeneration of field configurations to those of the zero-instanton sector this arbitrariness may be cancelled by a `topological counter-term' which we construct.