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Exploring curved superspace

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Abstract

We systematically analyze Riemannian manifolds \( \mathcal{M} \) that admit rigid supersymmetry, focusing on four-dimensional \( \mathcal{N} = {1} \) theories with a U(1) R symmetry. We find that \( \mathcal{M} \) admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on \( \mathcal{M} \). We then consider the restrictions imposed by the presence of additional supercharges. Two supercharges of opposite R-charge exist on certain fibrations of a two-torus over a Riemann surface. Upon dimensional reduction, these give rise to an interesting class of supersymmetric geometries in three dimensions. We further show that compact manifolds admitting two supercharges of equal R-charge must be hyperhermitian. Finally, four supercharges imply that \( \mathcal{M} \) is locally isometric to \( {\mathcal{M}_3} \times \mathbb{R} \), where \( {\mathcal{M}_3} \) is a maximally symmetric space.

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Authors and Affiliations

  1. Department of Physics, Princeton University, Princeton, NJ, 08544, U.S.A.

    Thomas T. Dumitrescu

  2. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Guido Festuccia & Nathan Seiberg

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  1. Thomas T. Dumitrescu
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  2. Guido Festuccia
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  3. Nathan Seiberg
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Correspondence to Thomas T. Dumitrescu.

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ArXiv ePrint: 1205.1115

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Dumitrescu, T.T., Festuccia, G. & Seiberg, N. Exploring curved superspace. J. High Energ. Phys. 2012, 141 (2012). https://doi.org/10.1007/JHEP08(2012)141

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