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Supersymmetric field theories on three-manifolds

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Abstract

We construct supersymmetric field theories on Riemannian three-manifolds \( \mathcal{M} \), focusing on \( \mathcal{N} \) = 2 theories with a U(1)R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flat-space supermultiplet containing the R-current and the energy-momentum tensor. The field theory on \( \mathcal{M} \) possesses a single supercharge if and only if \( \mathcal{M} \) admits an almost contact metric structure that satisfies a certain integrability condition. This may lead to global restrictions on \( \mathcal{M} \), even though we can always construct one supercharge on any given patch. We also analyze the conditions for the presence of additional supercharges. In particular, two supercharges of opposite R-charge exist on every Seifert manifold. We present general supersymmetric Lagrangians on \( \mathcal{M} \) and discuss their flat-space limit, which can be analyzed using the R-current supermultiplet. As an application, we show how the flat-space two-point function of the energy-momentum tensor in \( \mathcal{N} \) = 2 superconformal theories can be calculated using localization on a squashed sphere.

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Authors and Affiliations

  1. Weizmann Institute of Science, Rehovot, 76100, Israel

    Cyril Closset & Zohar Komargodski

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

    Thomas T. Dumitrescu

  3. Institute for Advanced Study, Princeton, NJ, 08540, U.S.A

    Guido Festuccia & Zohar Komargodski

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  1. Cyril Closset
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  2. Thomas T. Dumitrescu
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  3. Guido Festuccia
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  4. Zohar Komargodski
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Correspondence to Thomas T. Dumitrescu.

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ArXiv ePrint: 1212.3388

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Closset, C., Dumitrescu, T.T., Festuccia, G. et al. Supersymmetric field theories on three-manifolds. J. High Energ. Phys. 2013, 17 (2013). https://doi.org/10.1007/JHEP05(2013)017

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