Self-dual Skyrmions on the spheres S2N+1

Abstract

We construct self-dual sectors for scalar field theories on a (2N+2)-dimensional Minkowski space-time with the target space being the 2N+1-dimensional sphere S2N+1. The construction of such self-dual sectors is made possible by the introduction of an extra functional in the action that renders the static energy and the self-duality equations conformally invariant on the (2N+1)-dimensional spatial submanifold. The conformal and target-space symmetries are used to build an ansatz that leads to an infinite number of exact self-dual solutions with arbitrary values of the topological charge. The five-dimensional case is discussed in detail, where it is shown that two types of theories admit self-dual sectors. Our work generalizes the known results in the three-dimensional case that lead to an infinite set of self-dual Skyrmion solutions.