New Faddeev-Niemi type variables for static SU(3) Yang-Mills theory

TL;DR

This paper introduces new Faddeev-Niemi type variables for static SU(3) Yang-Mills theory, revealing a sigma model structure that could support knot-like excitations and a mass gap.

Contribution

It proposes novel variables that expose a sigma model structure in SU(3) Yang-Mills theory, extending previous models to potentially support topological excitations.

Findings

Identifies a sigma model with fields in SU(3)/(U(1)xU(1)) and SU(3)/(SU(2)xU(1))

Shows the energy functional is bounded by a topological invariant

Suggests the model may support knot-like excitations and a mass gap

Abstract

We propose new variables of Faddeev-Niemi type for static SU(3) Yang-Mills theory. These variables reveal a structure of a nonlinear sigma model, whose field variables are two chiral fields taking values in SU(3)/(U(1)xU(1)) and SU(3)/(SU(2)xU(1)). The nonlinear sigma model was introduced by Faddeev and Niemi as a natural extension of the Faddeev chiral model. Shabanov showed that the energy functional of the extended model is bounded from below by a topological invariant, and therefore may support knot-like excitations and a mass gap.