Symmetries of N = (1, 0) supergravity backgrounds in six dimensions

Authors: Sergei M. Kuzenko, Ulf Lindström, Emmanouil S. N. Raptakis and Gabriele Tartaglino-Mazzucchelli Preprint number: UUITP-53/20 Abstract:  General N = (1,0) supergravity-matter system in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) SU(2) superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of a given supergravity background. In particular, we introduce the notion of a conformal Killing spinor superfield εα, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector ξ and tensor ζ(n) superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we intro- duce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d’Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on conformally flat backgrounds.