Low-energy effective action in 5D, N=2 supersymmetric gauge theory

We construct $\mathcal{N}=2$ supersymmetric low-energy effective action of $5D, {\cal N}=2$supersymmetricYang-Millstheoryin$5D, {\cal N}=1$ harmonic superspace. It is obtained as a hypermultiplet completion of the leading $W \ln W$-terminthe${\cal N}=1$ SYM low-energy effective action by invoking the second implicit on-shell $\mathcal{N}=1$ supersymmetry. After passing to components, the $\mathcal{N}=2$ effective action constructed displays, along with other terms, the $SO(5)$-invariant $F^4\mathrm{/}{X}^3$ term. Though we specialize to the case of $SU(2)$ gauge group spontaneously broken to $U(1)$, our consideration is applicable to any gauge symmetry broken to some abelian subgroup.