Hamiltonian Reduction and Classical Extended Superconformal Algebras

TL;DR

This paper systematically constructs classical extended superconformal algebras via Hamiltonian reduction of affine Lie superalgebras, including the doubly extended N=4 algebra, and explores their free field representations and generalizations.

Contribution

It introduces a method to derive extended superconformal algebras from affine Lie superalgebras, including new algebraic structures like the doubly extended N=4 algebra.

Findings

Derived the doubly extended N=4 superconformal algebra from D(2|1;γ)

Provided free field representations and Miura transformations for these algebras

Discussed W-algebraic generalizations of the constructed algebras

Abstract

We present a systematic construction of classical extended superconformal algebras from the hamiltonian reduction of a class of affine Lie superalgebras, which include an even subalgebra $sl(2)$. In particular, we obtain the doubly extended $N=4$ superconformal algebra $\tilde{A}_{\gamma}$ from the hamiltonian reduction of the exceptional Lie superalgebra $D(2|1;\gamma/(1-\gamma))$. We also find the Miura transformation for these algebras and give the free field representation. A $W$-algebraic generalization is discussed.