Abstract
Calorons (periodic instantons) interpolate between monopoles and instantons, and their holonomy gives approximate Skyrmion configurations. We show that, for each caloron charge N⩽4, there exists a one-parameter family of calorons which are symmetric under subgroups of the three-dimensional rotation group. In each family, the corresponding symmetric monopoles and symmetric instantons occur as limiting cases. Symmetric calorons therefore provide a connection between symmetric monopoles, symmetric instantons and Skyrmions.
Highlights
Calorons are finite-action self-dual gauge fields in four dimensions, which are periodic in one of the four coordinates
The holonomy Ω of the gauge field in the t-direction is a map from R3 to the gauge group, and as such can serve as an approximation to Skyrmions [1]
This Letter demonstrates the existence of symmetric calorons of charge N, for N ≤ 4; they include, as limiting cases, symmetric monopoles and symmetric instantons
Summary
Calorons are finite-action self-dual gauge fields in four dimensions, which are periodic in one of the four coordinates. Special cases include instantons on R4 (where β → ∞) and BPS monopoles (where the gauge field is independent of t). This Letter demonstrates the existence of symmetric calorons of charge N , for N ≤ 4; they include, as limiting cases, symmetric monopoles and symmetric instantons.
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