Self-dual instanton and nonself-dual instanton-antiinstanton solutions in $d=4$ Yang-Mills theory

Details Self-dual instanton and nonself-dual instanton-antiinstanton solutions in $d=4$ Yang-Mills theory Self-dual instanton and nonself-dual instanton-antiinstanton solutions in $d=4$ Yang-Mills theory

2006-03-09

arxiv.org/abs/hep-th/0603071v1

Phys.Lett.B636:201-206,2006

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 5 Figures

Scientific paper

10.1016/j.physletb.2006.03.055

Subjecting the SU(2) Yang--Mills system to azimuthal symmetries in both the $x-y$ and the $z-t$ planes results in a residual subsystem described by a U(1) Higgs like model with two complex scalar fields on the quarter plane. The resulting instantons are labeled by integers $(m,n_1,n_2)$ with topological charges $q=\frac12 [1-(-1)^m]n_1n_2$. Solutions are constructed numerically for $m=1,2,3$ and a range of $n_1=n_2=n$. It is found that only the $m=1$ instantons are self-dual, the $m>1$ configurations describing composite instanton-antiinstanton lumps.

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