A pure Skyrme instanton

Abstract

The nuclear Skyrme model is considered in the extreme limit where the nucleon radius tends to infinity. In this limit only the Skyrme term in the action is significant. The model is then conformally invariant in dimension 4, and supports an instanton solution which can be constructed explicitly. The construction uses the conformal invariance and a certain symmetry reduction to reduce the model to the static phi^4 model in one dimension. The phi^4 kink solution gives the radial profile of the instanton, the kink position zero-mode corresponding to the instanton width.