Lie Superalgebra and Extended Topological Conformal Symmetry in Non-critical $W_{3}$ Strings

TL;DR

This paper presents a new free field realization of the N=2 super W_3 algebra via quantum Hamiltonian reduction, linking it to extended topological conformal symmetry in non-critical W_3 string theory.

Contribution

It introduces a novel realization of the super W_3 algebra using a specific affine Lie superalgebra and relates it to topological conformal symmetry in string theory.

Findings

New free field realization of N=2 super W_3 algebra

Connection established between W algebra and topological conformal symmetry

Applicable to non-critical W_3 string theory

Abstract

We obtain a new free field realization of $N=2$ super $W_{3}$ algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra $sl(3|2)^{(1)}$ associated with a non-standard $sl(2)$ embedding. After twisting and a similarity transformation, this $W$ algebra can be identified as the extended topological conformal algebra of non-critical $W_{3}$ string theory.