Superconformal $ \mathcal{N} = {3} $ SYM low-energy effective action

Abstract

We construct a manifestly $ \mathcal{N} = {3} $ supersymmetric low-energy effective action of $ \mathcal{N} = {3} $ super Yang-Mills theory. The effective action is written in the $ \mathcal{N} = {3} $ harmonic superspace and respects the full $ \mathcal{N} = {3} $ superconformal symmetry. On mass shell this action is responsible for the four-derivative terms in the $ \mathcal{N} = {4} $ SYM effective action, such as F 4/X 4 and its supersymmetric completions, while off shell it involves also higher- derivative terms. For constant Maxwell and scalar fields its bosonic part coincides, up to the F 6/X 8 order, with the bosonic part of the D3 brane action in the AdS5 × S 5 background. We also argue that in the sector of scalar fields it involves the correctly normalized Wess-Zumino term with the implicit SU(3) symmetry.