Effective sigma models and lattice Ward identities

TL;DR

This paper investigates the Faddeev-Niemi effective action for SU(2) Yang-Mills theory using lattice simulations, revealing that the generated ensemble cannot be fully described by the minimal Faddeev-Niemi model due to symmetry-breaking effects.

Contribution

It provides a lattice-based analysis of the Faddeev-Niemi model and demonstrates limitations of the minimal model in capturing the observed ensemble behavior.

Findings

Ensemble exhibits a mass gap of about 1 GeV.

Generated ensemble cannot be reproduced by the minimal Faddeev-Niemi action.

Adding explicit symmetry-breaking terms is necessary to match the ensemble.

Abstract

We perform a lattice analysis of the Faddeev-Niemi effective action conjectured to describe the low-energy sector of SU(2) Yang-Mills theory. To this end we generate an ensemble of unit vector fields ("color spins") n from the Wilson action. The ensemble does not show long-range order but exhibits a mass gap of the order of 1 GeV. From the distribution of color spins we reconstruct approximate effective actions by means of exact lattice Schwinger-Dyson and Ward identities ("inverse Monte Carlo"). We show that the generated ensemble cannot be recovered from a Faddeev-Niemi action, modified in a minimal way by adding an explicit symmetry-breaking term to avoid the appearance of Goldstone modes.