### Abstract

We use the manifestly N=2 supersymmetric, off-shell, harmonic (or twistor) superspace approach to solve the constraints implied by four-dimensional N=2 superconformal symmetry on the N=2 non-linear sigma-model target space, known as the special hyper-Kähler geometry. Our general solution is formulated in terms of a homogeneous (of degree two) function of unconstrained (analytic) Fayet-Sohnius hypermultiplet superfields. We also derive the improved (N=2 superconformal) actions for the off-shell (constrained) N=2 projective hypermultiplets, and relate them (via non-conformal deformations) to the asymptotically locally-flat (ALF) A_{k} and D_{k} series of the gravitational instantons. The same metrics describe Kaluza-Klein monopoles in M-theory, while they also arise in the quantum moduli spaces of N=4 supersymmetric gauge field theories with SU(2) gauge group and matter hypermultiplets in three spacetime dimensions. We comment on rotational isometries versus translational isometries in the context of N=2 NLSM in terms of projective hypermultiplets.

Original language | English |
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Pages (from-to) | 95-118 |

Number of pages | 24 |

Journal | Nuclear Physics B |

Volume | 582 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 28 Aug 2000 |

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### Keywords

- 11.10.Lm
- 11.15.Tk
- 11.30.Pb
- 12.60.Jv

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*582*(1-3), 95-118. https://doi.org/10.1016/S0550-3213(00)00252-2