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A supersymmetric extension of the Skyrme model was obtained recently, whichconsists of only the Skyrme term in the Nambu-Goldstone (pion) sectorcomplemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarzdimensional reduction yields a kinetic term in three or lower dimensions and apotential term in two dimensions, preserving supersymmetry. Euclidean solitons(instantons) are constructed in the supersymmetric Skyrme model. In fourdimensions, the soliton is an instanton first found by Speight. Scherk-Schwarzdimensional reduction is then performed once to get a 3-dimensional theory inwhich a 3d Skyrmion-instanton is found and then once more to get a 2d theory inwhich a 2d vortex-instanton is obtained. Although the last one is a globalvortex it has finite action in contrast to conventional theory. All of them arenon-BPS states breaking all supersymmetries.

Topological solitons in the supersymmetric Skyrme model