Non-relativistic supersymmetry on curved three-manifolds

DOI10.1007/JHEP07(2020)175zbMATH Open1451.83107arXiv2005.09001MaRDI QIDQ2215416

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Publication date: 11 December 2020

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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 Poincar'e disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds.

Full work available at URL: https://arxiv.org/abs/2005.09001

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