Superconformal Covariantization Of Superdifferential Operator On (1|1) Superspace And Classical N=2 W-superalgebras

TL;DR

This paper investigates the superconformal covariantization of superdifferential operators on (1|1) superspace, revealing that only odd-order operators can be covariantized, with transformations linked to supersymmetric Gelfand-Dickey brackets.

Contribution

It demonstrates that superdifferential operators of odd order can be covariantized under superconformal transformations, connecting these transformations to Hamiltonian flows of supersymmetric brackets.

Findings

Only odd-order superdifferential operators can be covariantized.

Superconformal transformations correspond to Hamiltonian flows.

Covariant form of odd-order operators is explicitly given.

Abstract

A study of the superconformal covariantization of superdifferential operators defined on $(1|1)$ superspace is presented. It is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order. In such a case, the action of superconformal transformation on the superdifferential operator is nothing but a hamiltonian flow defined by the corresponding supersymmetric second Gelfand-Dickey bracket. The covariant form of a superdifferential operator of odd order is given.