Canonical approach to 2D supersymmetric WZNW model coupled to supergravity

TL;DR

This paper develops a canonical framework for the 2D supersymmetric WZNW model coupled to supergravity, extending algebra representations and constructing an invariant action with local gauge symmetries.

Contribution

It introduces a covariant extension of the supersymmetric WZNW model using canonical methods, including explicit gauge transformations and algebra representations.

Findings

Extended super Kac-Moody and super Virasoro algebra representations.

Constructed a gauge-invariant action with local supersymmetry.

Provided explicit expressions for gauge transformations.

Abstract

Starting from the known representation of the Kac-Moody algebra in terms of the coordinates and momenta, we extend it to the representation of the super Kac-Moody and super Virasoro algebras. Then we use general canonical method to construct an action invariant under local gauge symmetries, where components of the super energy-momentum tensor $L_\pm$ and $G_\pm$ play the role of the diffeomorphisms and supersymmetries generators respectively. We obtain covariant extension of WZNW theory with respect to local supersymmetry as well as explicit expressions for gauge transformations.