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arXiv · 2601.08543

Topology of Calorons Re-examined

Atsushi Nakamula·Genki Sumiyama
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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.

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Atsushi Nakamula, Genki Sumiyama. 2026-01-13. Topology of Calorons Re-examined. https://doi.org/10.1063/5.0324583

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