Extended Superconformal Algebras and Free Field Realizations from Hamiltonian Reduction

TL;DR

This paper develops a method for deriving explicit classical and quantum extended superconformal algebras from affine Lie superalgebras using Hamiltonian reduction, gauge transformations, and quantum corrections.

Contribution

It provides a general framework for obtaining free field realizations of superconformal algebras through Hamiltonian reduction and gauge transformations.

Findings

Explicit formulas for classical and quantum extended superconformal algebras.

General expressions for free field realizations.

Inclusion of quantum corrections in the algebra derivations.

Abstract

We develop the method of the hamiltonian reduction of affine Lie superalgebras to obtain explicit and general expressions both for the classical and the quantum extended superconformal algebras. By performing the gauge transformation which connects the diagonal gauge with the Drinfeld-Sokolov gauge and considering the quantum corrections, we get generic expressions for the classical and quantum free field realizations of the algebras.