Skyrme model from 6d $\mathcal{N}$= (2,0) theory

We consider 5d Yang-Mills theory with a compact ADE-type gauge group $G$ on ${\mathbb{R}}^{3,1}\times \mathcal{I}$, where $\mathcal{I}$ is an interval. The maximally supersymmetric extension of this model appears after compactification on $S^1$ of 6d $\mathcal{N}$= (2,0) superconformal field theory on ${\mathbb R}^{3,1}\times S^2_2$,where$S^2_2\cong{\cal I}\times S^1$ is a two-sphere with two punctures. In the low-energy limit, when the length of $\mathcal{I}$ becomes small, the 5d Yang-Mills theory reduces to a nonlinear sigma model on ${\mathbb R}^{3,1}$withtheLiegroup$G$ as its target space. It contains an infinite tower of interacting fields whose leading term in the infrared is the four-derivative Skyrme term. A maximally supersymmetric generalization leading to a hyper-K"ahler sigma-model target space is briefly discussed.