Superconformally covariant operators and super W algebras

TL;DR

This paper investigates superdifferential operators covariant under superconformal transformations on super Riemann surfaces, revealing their origin from super M"obius covariant operators and exploring applications to super W algebras.

Contribution

It demonstrates that all superconformally covariant superdifferential operators of odd order derive from super M"obius covariant operators and provides a matrix representation with applications to super W algebras.

Findings

All such operators originate from super M"obius covariant operators.

A canonical matrix representation of these operators is constructed.

Applications to classical super W algebras are discussed.

Abstract

We study superdifferential operators of order $2n+1$ which are covariant with respect to superconformal changes of coordinates on a compact super Riemann surface. We show that all such operators arise from super M\"obius covariant ones. A canonical matrix representation is presented and applications to classical super W algebras are discussed.