### 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 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Exact hypermultiplet dynamics in four dimensions.** / Ketov, Sergei V.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Exact hypermultiplet dynamics in four dimensions

AU - Ketov, Sergei V.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

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U2 - 10.1016/S0370-2693(99)01221-6

DO - 10.1016/S0370-2693(99)01221-6

M3 - Article

VL - 469

SP - 136

EP - 144

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

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

SN - 0370-2693

IS - 1-4

ER -