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

Abstract

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

Keywords

• Extended Supersymmetry
• Superspaces
• Supersymmetric Effective Theories
• Supersymmetric Gauge Theory