Wess-Zumino term in the N=4 SYM effective action revisited

TL;DR

This paper revisits the Wess-Zumino term in the N=4 super Yang-Mills effective action, presenting new forms with various R-symmetry subgroups and analyzing their consistency across different superspace formulations.

Contribution

It provides explicit four-dimensional forms of the WZ term with different R-symmetry subgroups and discusses their compatibility with various superspace approaches.

Findings

WZ term with manifest SO(6) symmetry derived

SO(5) and SO(4) x SO(2) forms constructed in harmonic superspaces

No form with manifest SU(3) symmetry found

Abstract

The low-energy effective action for the N=4 super Yang-Mills on the Coulomb branch is known to include an SO(6)-invariant Wess-Zumino (WZ) term for the six scalar fields. For each maximal, non-anomalous subgroup of the SU(4) R-symmetry, we find a four-dimensional form of the WZ term with this subgroup being manifest. We then show that a recently proposed expression for the four-derivative part of the effective action in N=4 USp(4) harmonic superspace yields the WZ term with manifest SO(5) R-symmetry subgroup. The N=2 SU(2) harmonic superspace form of the effective action produces the WZ term with manifest SO(4) x SO(2). We argue that there is no four-dimensional form of the WZ term with manifest SU(3) R-symmetry, which is relevant for N=1 and N=3 superspace formulations of the effective action.