Global Supersymmetry on Curved Spaces in Various Dimensions

Abstract

We propose methods towards a systematic determination of d dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity point of view. In particular, by using appropriate gauged supergravities in various dimensions we show that supersymmetry can be defined in conformally flat spaces, such as non-compact hyperboloids $H^{n+1}$ and compact spheres $S^n$ or --by turning on appropriate Wilson lines corresponding to R-symmetry vector fields-- on $S^{1}x{S}^n$, with n<6. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres $S^d$ if d>5 (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification.

28 pages. Minor additions and more references

References in corpus (12)

• Notes on SUSY Gauge Theories on Three-Sphere
• Exact Results in D=2 Supersymmetric Gauge Theories
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• Supersymmetry on Curved Spaces and Holography
• Exploring Curved Superspace
• Supersymmetric Gauge Theories on the Five-Sphere
• Supersymmetry in Lorentzian Curved Spaces and Holography
• Exploring Curved Superspace (II)
• Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity
• Five-dimensional N = 1 AdS superspace: Geometry, off-shell multiplets and dynamics
• On Supersymmetric Gauge Theories on S^4 x S^1
• Exact results for perturbative partition functions of theories with SU(2|4) symmetry

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• Three-dimensional N=2 supergravity theories: From superspace to components
• A slow review of the AGT correspondence
• Rigid 6D supersymmetry and localization
• Symmetries of curved superspace in five dimensions
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• Supersymmetric backgrounds from 5d N=1 supergravity
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• Supersymmetry anomalies in new minimal supergravity
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• CFT in Conformally Flat Spacetimes
• (1,0) gauge theories on the six-sphere
• Self-consistency of Conformally Coupled ABJM Theory at the Quantum Level
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
• Equivariant and supersymmetric localization in QFT
• Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension
• Gauge theories with 16 supersymmetries on spheres