Knot topology in QCD

TL;DR

This paper explores the topological structures of classical vacuum solutions in QCD, classifies non-trivial configurations, and constructs exact solutions including knot and monopole structures, advancing understanding of QCD vacuum topology.

Contribution

It introduces a classification of QCD vacuum configurations via homotopy groups and constructs new exact classical solutions with knot and monopole topologies.

Findings

Explicit vacuum knot configurations classified by homotopy groups.

Exact non-static knot solutions in a CP^1 model.

Construction of knot-like solutions in SU(2) and SU(3) QCD.

Abstract

We consider topological structure of classical vacuum solutions in quantum chromodynamics. Topologically non-equivalent vacuum configurations are classified by non-trivial second and third homotopy groups for coset of the color group SU(N) (N=2,3) under the action of maximal Abelian stability group. Starting with explicit vacuum knot configurations we study possible exact classical solutions as vacuum excitations. Exact analytic non-static knot solution in a simple CP^1 model in Euclidean space-time has been obtained. We construct an ansatz based on knot and monopole topological vacuum structure for searching new solutions in SU(2) and SU(3) QCD. We show that singular knot-like solutions in QCD in Minkowski space-time can be naturally obtained from knot solitons in integrable CP^1 models. A family of Skyrme type low energy effective theories of QCD admitting exact analytic solutions with non-vanishing Hopf charge is proposed.