Reflections on Topology - Viewpoints on Abelian Projections

Details Reflections on Topology - Viewpoints on Abelian Projections Reflections on Topology - Viewpoints on Abelian Projections

2001-09-19

arxiv.org/abs/hep-th/0109148v1

Nucl.Phys.Proc.Suppl. 108 (2002) 3-11

Physics

High Energy Physics

High Energy Physics - Theory

9 p, 5 figs, talks presented at workshops in Cairns and Trento

Scientific paper

10.1016/S0920-5632(02)01298-7

This talk discusses two topological features in non-abelian gauge theories, related by the notion of abelian projection and the Hopf invariant. Minimising the energy of the non-linear sigma model with a Skyrme-like term (the Faddeev-Niemi model), can be identified with a non-linear maximal abelian gauge fixing of the SU(2) gauge vacua with a winding number equal to the Hopf invariant. In the context of abelian projection the Hopf invariant can also be associated to a monopole world line, through the Taubes winding, measuring its contribution to topological charge. Calorons with non-trivial holonomy provide an explicit realisation. We discuss the identification of its constituent monopoles through degenerate eigenvalues of the Polyakov loop (the singularities or defects of the abelian projection). It allows us to study the correlation between the defect locations and the explicit constituent monopole structure, through a specific SU(3) example.

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