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Periodic instantons with non-trivial holonomy. (English) Zbl 0978.53512
Summary: We present the detailed derivation of the charge-1 periodic instantons - or calorons - with non-trivial holonomy for SU(2)2. We use a suitable combination of the Nahm transformation and ADHM techniques. Our results rely on our ability to compute explicitly the relevant Green’s function in terms of which the solution can be conveniently expressed. We also discuss the properties of the moduli space, 3 ×𝕊 1 × Taub-NUT/ 2 and its metric, relating the holonomy to the Taub-NUT mass parameter. We comment on the monopole constituent description of these calorons, how to retrieve topological charge in the context of abelian projection and possible applications to QCD.
MSC:
53C80Applications of global differential geometry to physics
81T13Yang-Mills and other gauge theories
53C07Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
53C29Issues of holonomy