Global supersymmetry on curved spaces in various dimensions Original Research Article

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 image and compact spheres image or – by turning on appropriate Wilson lines corresponding to R-symmetry vector fields – on image, with image. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres image if image (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification.