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

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,n1,n2) with topological charges q=12[1−(−1)m]n1n2. Solutions are constructed numerically for m=1,2,3 and a range of n1=n2=n. It is found that only the m=1 instantons are self-dual, the m>1 configurations describing composite instanton-antiinstanton lumps.