### 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.

Original language | English |
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Pages (from-to) | 333-388 |

Number of pages | 56 |

Journal | Physics of Particles and Nuclei |

Volume | 48 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 May 2017 |

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### Cite this

*Physics of Particles and Nuclei*,

*48*(3), 333-388. https://doi.org/10.1134/S1063779617030042