Topology of the O(3) non-linear sigma model under the gradient flow

TL;DR

This paper investigates the behavior of topological charge in the O(3) non-linear sigma model under the gradient flow, revealing persistent divergence of topological susceptibility even with the flow, contrasting with lattice QCD results.

Contribution

It introduces a θ-term in the NLSM and analyzes topological charge evolution under the gradient flow, highlighting divergence issues not mitigated by the flow.

Findings

Divergence of topological susceptibility persists under gradient flow.

Gradient flow does not remove ultraviolet divergences in NLSM.

Behavior differs from lattice QCD where flow removes divergences.

Abstract

The O(3) non-linear sigma model (NLSM) is a prototypical field theory for QCD and ferromagnetism, and provides a simple system in which to study topological effects. In lattice QCD, the gradient flow has been demonstrated to remove ultraviolet singularities from the topological susceptibility. In contrast, lattice simulations of the NLSM find that the topological susceptibility diverges in the continuum limit, even in the presence of the gradient flow. We introduce a $\theta$-term and analyze the topological charge as a function of $\theta$ under the gradient flow. Our results show that divergence persists in the presence of the flow, even at non-zero $\theta$.