Quantum Hamiltonian Reduction in Superspace Formalism

TL;DR

This paper extends quantum Hamiltonian reduction to N=1 affine Lie superalgebras within superspace formalism, explicitly constructing superconformal algebra generators and linking supersymmetric and non-supersymmetric reductions.

Contribution

It introduces a method to perform quantum Hamiltonian reduction in superspace, connecting supersymmetric and non-supersymmetric Lie superalgebras, with explicit generator constructions.

Findings

Constructed super energy-momentum tensor and generators of spin 1 and 1/2.

Reduced supersymmetric Hamiltonian to non-supersymmetric case under gauge choice.

Explicitly derived superconformal and related algebra generators.

Abstract

Recently the quantum hamiltonian reduction was done in the case of general $s\ell(2)$ embeddings into Lie algebras and superalgebras. In this paper we extend the results to the quantum hamiltonian reduction of $N=1$ affine Lie superalgebras in the superspace formalism. We show that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum hamiltonian reduction reduces to quantum hamiltonian reduction of non-supersymmetric Lie superalgebras. We construct explicitly the super energy-momentum tensor, as well as all generators of spin 1 (and $\hf$); thus we construct explicitly all generators in the superconformal, quasi-superconformal and $\Z_2 \times \Z_2$ superconformal algebras.