Knot topology in 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.
Keywords
Cite
@article{arxiv.1302.3527,
title = {Knot topology in QCD},
author = {L. P. Zou and P. M. Zhang and D. G. Pak},
journal= {arXiv preprint arXiv:1302.3527},
year = {2013}
}
Comments
9 pages, final version accepted by PLB