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Non-relativistic supersymmetry on curved three-manifolds

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  • Published: 24 July 2020
  • Volume 2020, article number 175, (2020)
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Non-relativistic supersymmetry on curved three-manifolds
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  • E.A. Bergshoeff1,2,
  • A. Chatzistavrakidis  ORCID: orcid.org/0000-0002-9326-98713,
  • J. Lahnsteiner1,
  • L. Romano1 &
  • …
  • J. Rosseel4 

  • 336 Accesses

  • 6 Citations

  • 2 Altmetric

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A preprint version of the article is available at arXiv.

Abstract

We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on Lorentzian manifolds and the Killing spinor equations that their supersymmetry parameters obey. This gives rise to a set of algebraic and differential Killing spinor equations that are obeyed by the supersymmetry parameters of the resulting three-dimensional non-relativistic field theories. We derive necessary and sufficient conditions that determine whether a Newton-Cartan background admits non-trivial solutions of these Killing spinor equations. Two classes of examples of Newton-Cartan backgrounds that obey these conditions are discussed. The first class is characterised by an integrable foliation, corresponding to so-called twistless torsional geometries, and includes manifolds whose spatial slices are isomorphic to the Poincaŕe disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds.

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Authors and Affiliations

  1. Van Swinderen Institute, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands

    E.A. Bergshoeff, J. Lahnsteiner & L. Romano

  2. Erwin Schrödinger International Institute for Mathematics and Physics, Boltzmanngasse 9, A-1090, Vienna, Austria

    E.A. Bergshoeff

  3. Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia

    A. Chatzistavrakidis

  4. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria

    J. Rosseel

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Correspondence to A. Chatzistavrakidis.

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Bergshoeff, E., Chatzistavrakidis, A., Lahnsteiner, J. et al. Non-relativistic supersymmetry on curved three-manifolds. J. High Energ. Phys. 2020, 175 (2020). https://doi.org/10.1007/JHEP07(2020)175

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  • Received: 27 May 2020

  • Accepted: 04 July 2020

  • Published: 24 July 2020

  • DOI: https://doi.org/10.1007/JHEP07(2020)175

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Keywords

  • Supersymmetric Effective Theories
  • Supergravity Models
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