Topology of Calorons Re-examined

Abstract

We reconsider the detailed structure of the topological character of the instantons in pure Yang-Mills theory on $S^1\times {\mathbb{R}}^3$, known as calorons. We argue that the standard formula for the second Chern number requires modification, as revealed by explicit analytic consideration. For concreteness, we compute the second Chern number of the Harrington-Shepard caloron of the two-dimensional special unitary gauge group ($\mathrm{SU}(2)$) with unit topological charge in several gauges. The general formula is shown to remain valid even when the gauge connection is in a singular gauge. The gauge dependence of the magnetic charge is also discussed.

23 pages, no figure

References in corpus (5)

• Generalized Global Symmetries
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• The gaugino condensate from asymmetric four-torus with twists
• Large scale and large period limits of symmetric calorons
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$