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arXiv · 1302.3527

Knot topology in QCD

L. P. Zou·P. M. Zhang·D. G. Pak
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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.

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L. P. Zou, P. M. Zhang, D. G. Pak. 2013-08-28. Knot topology in QCD. https://doi.org/10.1016/j.physletb.2013.08.037

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