BRST operators for W algebras

TL;DR

This paper explores the construction of BRST operators for W-algebras, specifically W_3 and W_3^(2), using non-canonical ghosts to handle their non-linear structure, resulting in a cubic form of the BRST operator.

Contribution

It introduces a method to construct BRST operators for non-linear W-algebras using non-canonical ghosts, highlighting their cubic structure.

Findings

BRST operators for W_3 and W_3^(2) are cubic in form.

Non-canonical ghosts are effective for non-linear algebra quantization.

The approach simplifies the BRST construction for complex algebras.

Abstract

The study of quantum Lie algebras motivates a use of non-canonical ghosts and anti-ghosts for non-linear algebras, like W-algebras. This leads, for the W_3 and W_3^(2) algebras, to the BRST operator having the conventional cubic form.