Viewpoints on Abelian projections

by Pierre VAN BAAL (Leiden University)

Thursday 7 Jun 2001, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

At finite temperature the Abelian projected Polyakov gauge can be applied to the exact caloron solutions with non-trivial holonomy to locate its constituent monopoles. Topology requires the presence of Abelian projected monopoles, but an SU(3) example makes clear these need not be correlated to energy density. The same calorons can also be studied in the maximal Abelian gauge relating the topology to a Hopf invariant. It is this Hopf invariant, which also classifies the non-trivial knot solutions that appear in the Faddeev-Niemi non-linear sigma model. We discuss a surprising reinterpretation of this model: knots as classical vacua in a non-linear maximal Abelian projection.