New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, SYM superfield constraints are solved terms on-shell $\mathcal {N}=2$ harmonic superfields. Such an approach provides convenient tool constructing manifestly invariants and further rewriting them $\mathcal{N}= 2$ superspace. particular, we present form leading term effective action which was known previously $\mathcal{N}=2$ formulation.