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

摘要

We consider 5d Yang–Mills theory with a compact ADE-type gauge group G on R 3 , 1 × I , where I is an interval. The maximally supersymmetric extension of this model appears after compactification on S 1 of 6d N = ( 2 , 0 ) superconformal field theory on R 3 , 1 × S 2 2 , where S 2 2 ? I × S 1 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 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?hler sigma-model target space is briefly discussed.