Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry

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.

53 pages, v2: refs added, typos correction, v3: refs added, typos corrections and linguistic modifications in sec. 2 for readability, v4: Acknowledgement modified

References in corpus (3)

• Supersymmetric Gauge Theories on the Five-Sphere
• 3d Chern-Simons Theory from M5-branes
• 3d TQFT from 6d SCFT

Cited by in corpus (17)

• 5d Partition Functions with A Twist
• Supersymmetric gauge theories on squashed five-spheres and their gravity duals
• Supersymmetric Rényi Entropy in Five Dimensions
• Symmetries of curved superspace in five dimensions
• Introduction to localization in quantum field theory
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Supersymmetric gauge theories on five-manifolds
• N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$
• Supersymmetric backgrounds from 5d N=1 supergravity
• Review of localization for 5d supersymmetric gauge theories
• Supersymmetric solutions to Euclidean Romans supergravity
• Rigid Supersymmetry from Conformal Supergravity in Five Dimensions
• Supersymmetry anomalies in new minimal supergravity
• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions