Calorons in Weyl Gauge

We demonstrate by explicit construction that while the untwisted Harrington-Shepard caloron $A_{\mu }$ is manifestly periodic in Euclidean time, with period $\beta =\frac{1}{T}$, 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 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.