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Self-dual instanton and non-self-dual instanton–antiinstanton solutions in d=4 Yang–Mills theory

Eugen Radu, D.H. Tchrakian

2006
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Physics Letters B
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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 $m>1$
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... tions describing composite instanton-antiinstanton lumps.

doi:10.1016/j.physletb.2006.03.055
fatcat:vo4nsim475ewpeyqj5pakm52c4