### Abstract

We use N = 2 harmonic and projective superspaces to formulate the most general 'Ansatz' for the SU(2)_{R}-invariant hypermultiplet low-energy effective action (LEEA) in four dimensions, which describes the two-parametric family of the hyper-Kähler metrics generalizing the Atiyah-Hitchin metric. We then demonstrate in the very explicit and manifestly N = 2 supersymmetric way that the (magnetically charged, massive) single hypermultiplet LEEA in the underlying non-abelian N = 2 supersymmetric quantum field theory can receive both perturbative (e.g., in the Coulomb branch) and non-perturbative (e.g., in the Higgs branch) quantum corrections. The manifestly N= 2 supersymmetric Feynman rules in harmonic superspace can be used to calculate the perturbative corrections described by the Taub-NUT metric. The non-perturbative corrections (due to instantons and anti-instantons) can be encoded in terms of an elliptic curve, which is very reminiscent to the Seiberg-Witten theory. Our four-dimensional results agree with the three-dimensional Seiberg-Witten theory and instanton calculations.

Original language | English |
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Pages (from-to) | 136-144 |

Number of pages | 9 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 469 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 1 Jan 1999 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics