Self-Dual Skyrmions on the Spheres $S^{2N+1}$

We construct self-dual sectors for scalar field theories on a $(2N+2)$-dimensional Minkowski space-time with target space being the $2N+1$-dimensional sphere $S^{2N+1}$. The construction of such self-dual sectors is made possible by the introduction of an extra functional on 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 leads to an infinite set of self-dual Skyrmion solutions.