Through a careful analysis of this cohomology,Īnd of the renormalization group in curved spacetime, we establish preciseĬriteria which ensure that all conformal supersymmetries are preserved at the These identities allow us to recast the problem in terms of theĬohomology of the BRST operator. S-matrix and show that such products obey certain Ward identities in curved Renormalization scheme for time-ordered products that enter the perturbative when theīRST operator commutes with the perturbatively defined S-matrix, which ensures In particular, we examine the conditions necessary forĬonformal supersymmetries to be preserved at the quantum level, i.e. We then consider the corresponding perturbative Process, we elucidate the general framework of cohomological algebra which Theories and derive an appropriate BRST operator in curved spacetime. We construct theĬonformal symmetry superalgebras which describe classical symmetries of these Obtain a class of field theories with extended rigid conformal supersymmetry onĪny Lorentzian four-manifold admitting twistor spinors.

We comment on the implications of our results for holography.īy conformally coupling vector and hyper multiplets in Minkowski space, we This is equivalent to the vanishing of a superspace Weyl The term proportional to the central charge c vanishes, both in the trace and Supercharges of opposite R-charge, supersymmetry of the background implies that Particular, in Lorentzian signature, or in the presence of two Euclidean Theories simplify, with the trace anomaly becoming purely topological. This relation, the trace and R-current anomalies of superconformal field Part of the vector field-strength is fixed by the Weyl tensor. Supercharges of opposite R-charge are preserved, otherwise the (anti-)self-dual In Euclidean signature, the same holds if two The background vector field coupling to the R-current is determined by the Weyl We study the consequences of unbroken rigid supersymmetry of four-dimensionalįield theories placed on curved manifolds.

Curved space supersymmetry in 2d