The low-energy N=4 SYM effective action in diverse harmonic superspaces

TL;DR

This paper reviews various harmonic superspace methods to construct and analyze the low-energy effective action in N=4 super Yang-Mills theory, emphasizing different supersymmetries and symmetries to simplify the formulation.

Contribution

It introduces new superspace constructions for the N=4 SYM effective action that manifest different R-symmetry subgroups, simplifying the action's form.

Findings

Effective action simplifies in superspaces with manifest non-anomalous SU(4) subgroups.

Supersymmetric completions of F^4/X^4 and Wess-Zumino terms are constructed.

Approaches employ N=4 supersymmetry and superconformal symmetry for restoration.

Abstract

We review various superspace approaches to the description of the low-energy effective action in N=4 super Yang-Mills (SYM) theory. We consider the four-derivative part of the low-energy effective action in the Coulomb branch. The typical components of this effective action are the gauge field F^4/X^4 and the scalar field Wess-Zumino terms. We construct N=4 supersymmetric completions of these terms in the framework of different harmonic superspaces supporting N=2,3,4 supersymmetries. These approaches are complementary to each other in the sense that they make manifest different subgroups of the total SU(4) R-symmetry group. We show that the effective action acquires an extremely simple form in those superspaces which manifest the non-anomalous maximal subgroups of SU(4). The common characteristic feature of our construction is that we restore the superfield effective actions exclusively by employing the N=4 supersymmetry and/or superconformal PSU(2,2|4) symmetry.