We demonstrate by explicit construction that while the untwisted Harrington-Shepard caloron $A_{\mu }$ is manifestly periodic in Euclidean time, with a period $\beta =1/T,$ when transformed to the Weyl ${(A}_0=0)$ gauge, the caloron gauge field $A_i$ is periodic only up to a large gauge transformation, with the winding number equal to the caloron’s topological charge. This helps clarify the tunneling interpretation of these solutions, and their relation to Chern-Simons numbers and winding numbers.

• Received 21 November 2000

DOI:https://doi.org/10.1103/PhysRevD.63.085004