Skyrme model from 6d $\cal N$= (2,0) theory

Abstract

We consider 5d Yang-Mills theory with a compact ADE-type gauge group $G$ on ${\mathbb R}^{3,1}\times{\cal I}$, where $\cal I$ is an interval. The maximally supersymmetric extension of this model appears after compactification on $S^1$ of 6d $\cal N$= (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 $\cal I$ becomes small, the 5d Yang-Mills theory reduces to a nonlinear sigma model on ${\mathbb R}^{3,1}$ with the Lie group $G$ 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.