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

Abstract

We consider 5d Yang–Mills theory with a compact ADE-type gauge group G on R3,1×I, where I is an interval. The maximally supersymmetric extension of this model appears after compactification on S1 of 6d N=(2,0) superconformal field theory on R3,1×S2 2, where S2 2≅I×S1 is a two-sphere with two punctures. In the low-energy limit, when the length of I becomes small, the 5d Yang–Mills theory reduces to a nonlinear sigma model on R3,1 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-Kähler sigma-model target space is briefly discussed.