Abstract
We consider 3d superconformal field theories on a branched covering of a three-sphere. The Rényi entropy of a CFT is given by the partition function on this space, but conical singularities break the supersymmetry preserved in the bulk. We turn on a compensating R-symmetry gauge field and compute the partition function using localization. We define a supersymmetric observable, called the super Rényi entropy, parametrized by a real number q. We show that the super Rényi entropy is duality invariant and reduces to entanglement entropy in the q → 1 limit. We provide some examples.