Superconformal hypermultiplets in superspace

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7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)95-118
Number of pages24
JournalNuclear Physics B
Issue number1-3
Publication statusPublished - 28 Aug 2000


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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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