Hamiltonian Reduction of Super Osp(1,2)} and Sl(2,1) Kac-Moody Algebras

TL;DR

This paper develops a supercovariant Hamiltonian reduction framework for super OSp(1,2) and SL(2,1) Kac-Moody algebras, utilizing Wakimoto and free field constructions to connect to Virasoro and superconformal symmetries.

Contribution

It introduces a supercovariant extension of the Drinfeld-Sokolov Hamiltonian reduction for specific superalgebras, linking Wakimoto constructions to superconformal algebras.

Findings

Constructed Wakimoto representations for super OSp(1,2) and SL(2,1) Kac-Moody algebras.

Derived free field representations of associated WZW models.

Established a supercovariant Hamiltonian reduction connecting to Virasoro and superconformal algebras.

Abstract

We present the Wakimoto construction of the super OSp(1,2) and SL(2,1) Kac-Moody algebras and the free field representation of the corresponding WZW models. After imposing suitable constraints, we can lead the Feigin-Fuchs representation of Virasoro algebras and coadjoint actions ofthe N=1 and N=2 conformal symmetries. This formulation corresponds to a supercovariant extension of the Drinfeld and Sokolov Hamiltonian reduction.