SELF-DUAL SUPERGRAVITIES

Abstract

The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler 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'.

14 pages, latex file

References in corpus (3)

• Self-Dual N=8 Supergravity as Closed N=2(4) Strings
• The matreoshka of supersymmetric self-dual theories
• Self-Dual Gravity Revisited

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• N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory
• Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
• Four Dimensional Integrable Theories
• An action of N=8 self-dual supergravity in ultra-hyperbolic harmonic superspace
• String-induced Yang-Mills coupling to self-dual gravity
• On pseudo-hyperkähler prepotentials
• Unravelling the On-shell Constraints of Self-dual Supergravity Theories