### 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 |
---|---|

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 |

### Fingerprint

### 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

**Superconformal hypermultiplets in superspace.** / Ketov, Sergei V.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 582, no. 1-3, pp. 95-118. https://doi.org/10.1016/S0550-3213(00)00252-2

}

TY - JOUR

T1 - Superconformal hypermultiplets in superspace

AU - Ketov, Sergei V.

PY - 2000/8/28

Y1 - 2000/8/28

N2 - 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) Ak and Dk 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.

AB - 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) Ak and Dk 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.

KW - 11.10.Lm

KW - 11.15.Tk

KW - 11.30.Pb

KW - 12.60.Jv

UR - http://www.scopus.com/inward/record.url?scp=0034726219&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034726219&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(00)00252-2

DO - 10.1016/S0550-3213(00)00252-2

M3 - Article

VL - 582

SP - 95

EP - 118

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-3

ER -