Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-01-16
Nucl.Phys. B444 (1995) 381-400
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, latex file
Scientific paper
10.1016/0550-3213(95)00139-J
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'.
Devchand Ch.
Ogievetsky V.
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