Instantons and Magnetic Monopoles on $R^3\times S^1$ with Arbitrary Simple Gauge Groups

Details Instantons and Magnetic Monopoles on $R^3\times S^1$ with Arbitrary Simple Gauge Groups Instantons and Magnetic Monopoles on $R^3\times S^1$ with Arbitrary Simple Gauge Groups

1998-02-03

arxiv.org/abs/hep-th/9802012v1

Phys.Lett. B426 (1998) 323-328

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTex file, no figure

Scientific paper

10.1016/S0370-2693(98)00283-4

We investigate Yang-Mills theories with arbitrary gauge group on $R^3\times S^1$, 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 $S^1$ coordinate dependent magnetic monopole solutions in $G_2,F_4,E_8$.

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