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

TL;DR

This paper introduces a new bi-harmonic superspace formulation for 4D, N=4 SYM theory, enabling easier construction of supersymmetric invariants and rewriting known effective action terms in this framework.

Contribution

It develops a novel bi-harmonic superspace approach that solves superfield constraints using on-shell N=2 harmonic superfields, facilitating manifest N=4 supersymmetry.

Findings

Formulation of N=4 SYM in bi-harmonic superspace.

Representation of the leading effective action term in N=4 superspace.

Simplification of constructing supersymmetric invariants.

Abstract

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