Super Covering Maps

Abstract

We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of superconformal field theories, as well as in the hybrid formalism for tensionless string theory on ${\text{AdS}}_3\times S^3\times {\mathbb{T}}^4$. In the former, they can be used to calculate correlators in a manifestly supersymmetric way, while in the latter they solve Ward identities of correlators with spacetime supersymmetry.

35+12 pages, v2: added a discussion of the RNS formalism, expanded higher genus discussion, added references; matches published version