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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-dualsectors is made possible by the introduction of an extra functional on theaction that renders the static energy and the self-duality equationsconformally invariant on the $(2N+1)$-dimensional spatial submanifold. Theconformal and target space symmetries are used to build an ansatz that leads toan infinite number of exact self-dual solutions with arbitrary values of thetopological charge. The five dimensional case is discussed in detail where itis shown that two types of theories admit self dual sectors. Our workgeneralizes the known results in the three-dimensional case that leads to aninfinite set of self-dual Skyrmion solutions.

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