Free Field Representations of Extended Superconformal Algebras

TL;DR

This paper develops free field representations for extended superconformal algebras derived from affine Lie superalgebras, providing explicit formulas, BRST formalism application, and analysis of screening operators and singular vectors.

Contribution

It introduces a systematic method to obtain free field (Feigin-Fuchs) representations of extended superconformal algebras from affine Lie superalgebras, including explicit formulas and structural insights.

Findings

Derived Poisson bracket structures at the classical level.

Constructed free field representations using BRST formalism.

Analyzed screening operators and singular vectors in the free field framework.

Abstract

We study the classical and quantum $G$ extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson bracket structure of the algebra. At the quantum level we get free field (Feigin-Fuchs) representations of the algebra by using the BRST formalism and the free field realization of the affine Lie superalgebra. In particular we get the free field representation of the $sl(2)\oplus sp(2N)$ extended superconformal algebra from the Lie superalgebra $osp(4|2N)$. We also discuss the screening operators of the algebra and the structure of singular vectors in the free field representation.