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arXiv · 1308.1567

Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry

Yiwen Pan
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Abstract

In this note we generalize the methods of [1][2][3] to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity. The existence of 1 pair of solutions is related to almost contact metric structures. We also discuss special cases related to $M = S1 \times M4$, which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kahler. When there are 2 pairs of solutions, the closure of the isometry sub-algebra generated by the solutions requires M to be S3 or T3-fibration over a Riemann surface. 4 pairs of solutions pin down the geometry of M to very few possibilities. Finally, we propose a new supersymmetric theory for N = 1 vector multiplet on K-contact manifold admitting solutions to the Killing spinor equation.

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Yiwen Pan. 2015-05-29. Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry. https://doi.org/10.1007/jhep05(2014)041

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