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Pseudo-Hyperkähler Geometry and Generalized Kähler Geometry

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Abstract

We discuss the conditions for additional supersymmetry and twisted super-symmetry in N = (2, 2) supersymmetric nonlinear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show that these solutions correspond to a bi-hermitian metric of signature (2, 2) and a pseudo-hyperkähler geometry of the target space.

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  1. Division for Theoretical Physics, Department of Physics and Astronomy, Uppsala University, Box 803, 751 08, Uppsala, Sweden

    Malin Göteman & Ulf Lindström

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  1. Malin Göteman
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  2. Ulf Lindström
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Correspondence to Ulf Lindström.

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Göteman, M., Lindström, U. Pseudo-Hyperkähler Geometry and Generalized Kähler Geometry. Lett Math Phys 95, 211–222 (2011). https://doi.org/10.1007/s11005-010-0456-7

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  • DOI: https://doi.org/10.1007/s11005-010-0456-7

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