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

Eugen Radu, D.H. Tchrakian
2006 Physics Letters B  
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 $m>1$
more » ... tions describing composite instanton-antiinstanton lumps.
doi:10.1016/j.physletb.2006.03.055 fatcat:vo4nsim475ewpeyqj5pakm52c4