Super Covering Maps

TL;DR

This work introduces super covering maps, analytic maps between super Riemann surfaces that generalise branched coverings to supersymmetry. The authors demonstrate how these maps naturally encode twisted sectors and correlators in symmetric product orbifolds of superconformal field theories, and how they solve Ward identities in the string-theory context, both in the RNS and hybrid formalisms for tensionless strings on AdS3×S3×T4. They develop the formalism for genus-zero and higher-genus coverings, treat Ramond punctures, and provide explicit lifting rules for fields and twist operators, along with concrete examples of three-point and four-point correlators. The work points toward a unified geometric mechanism underlying supersymmetric AdS3/CFT2 holography and suggests future avenues to realize simultaneous worldsheet and spacetime supersymmetry within a single geometric framework.

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.