Exact N=4 Supersymmetric Low-Energy Effective Action in N=4 Super-Yang-Mills Theory

TL;DR

This paper constructs the exact low-energy effective action of N=4 Super-Yang-Mills theory, demonstrating that only logarithmic potentials compatible with N=4 supersymmetry can occur, using a formulation that reveals hidden supersymmetry.

Contribution

It explicitly completes known N=2 non-holomorphic potentials to N=4 supersymmetric form, providing the first exact low-energy effective action in N=4 SYM theory.

Findings

Non-holomorphic potentials ln W ln  W can be completed to N=4 supersymmetry.

Non-logarithmic potentials cannot be extended to N=4 supersymmetry.

The exact N=4 supersymmetric low-energy effective action is obtained.

Abstract

We review a recent progress in constructing the low-energy effective action of N=4 SYM theory. This theory is formulated in terms of N=2 harmonic superfields corresponding to N=2 vector multiplet and hypermultiplet. Such a formulation possesses the manifest N=2 supersymmetry and an extra hidden on-shell supersymmetry. Exploring the hidden N=2 supersymmetry we proved that the known non-holomorphic potentials of the form ln W ln \bar{W} can be explicitly completed by the appropriate hypermultiplet-dependent terms to the entire N=4 supersymmetric form. The non-logarithmic effective potentials do not admit an N=4 completion and, hence, such potentials cannot occur in N=4 supersymmetric theory. As a result we obtain the exact N=4 supersymmetric low-energy effective action in N=4 SYM theory.