Chand Devchand, Viktor Ogievetsky
Self-Dual Supergravities
Preprint series: ESI preprints

MSC:

58A50 Supermanifolds and graded manifolds, See also {14A22,

81T60 Supersymmetric field theories

83E50 Supergravity

32C11 Complex supergeometry, See also {14A22, 14M30, 58A50}

Abstract: The N-extended supersymmetric self-dual Poincar\'e supergravity
equations provide a natural local description of supermanifolds
possessing hyperk\"ahler structure. These equations admit an economical
formulation in chiral superspace. A reformulation in harmonic superspace
encodes self-dual supervielbeins and superconnections in a graded
skew-symmetric supermatrix superfield prepotential satisfying generalised
Cauchy-Riemann conditions. A recipe is presented for extracting explicit
self-dual supervielbeins and superconnections from such `analytic'
prepotentials. We demonstrate the method by explicitly decoding a
simple example of superfield prepotential, analogous to that corresponding
to the Taub-NUT solution. The superspace we thus construct is an
interesting $N=2$ supersymmetric deformation of flat space, having flat
`body' and constant curvature `soul'.

Keywords: supersymmetry, supergravity, hyperkaehler structure