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Hyperkähler metrics and supersymmetry

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Abstract

We describe two constructions of hyperkähler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinear σ-models, but can be described entirely geometrically. In this general setting, we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry, along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, 24-29 St. Giles, OX1 3LB, Oxford, United Kingdom

    N. J. Hitchin

  2. Institute of Theoretical Physics, University of Stockholm, Vanadisvägen 9, S-11346, Stockholm, Sweden

    A. Karlhede & U. Lindström

  3. Institute for Theoretical Physics, State University of New York, 11794, Stony Brook, NY, USA

    M. Roček

Authors
  1. N. J. Hitchin
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  2. A. Karlhede
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  3. U. Lindström
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  4. M. Roček
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Additional information

Communicated by L. Alvarez-Gaumé

Supported by the Swedish Natural Science Research Council

Research supported by the National Science Foundation under Contract No. PHY 81 09110 A-01 and PHY 85-07627

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Hitchin, N.J., Karlhede, A., Lindström, U. et al. Hyperkähler metrics and supersymmetry. Commun.Math. Phys. 108, 535–589 (1987). https://doi.org/10.1007/BF01214418

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  • DOI: https://doi.org/10.1007/BF01214418

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