Instantons and magnetic monopoles on R3×S1 with arbitrary simple gauge groups

Abstract

We investigate Yang-Mills theories with arbitrary gauge group on R3×S1, whose symmetry is spontaneously broken by the Wilson loop. We show that instantons are made of fundamental magnetic monopoles, each of which has a corresponding root in the extended Dynkin diagram. The number of constituent magnetic monopoles for a single instanton is the dual Coxeter number of the gauge group, which also accounts for the number of instanton zero modes. In addition, we show that there exists a novel type of the S1 coordinate dependent magnetic monopole solutions in G2,F4,E8.