A Derivation of the BRST Operator for Non-Critical W-Strings

TL;DR

This paper derives the BRST operator for non-critical W-strings using a Lagrangian approach, revealing a closed gauge algebra from matter and Toda systems, and proposes a new method to construct critical W_3 strings.

Contribution

It introduces a derivation of the BRST charge for non-critical W-strings from a Lagrangian perspective and presents a novel construction method for critical W_3 strings.

Findings

The combination of matter and Toda systems forms a closed gauge algebra.

A new approach to construct critical W_3 strings is proposed.

The gauge algebra is of the soft type, despite initial appearances.

Abstract

We derive the recently proposed BRST charge for non-critical W strings from a Lagragian approach. The basic observation is that, despite appearances, the combination of two classical ``matter'' and ``Toda'' w_3 systems leads to a closed modified gauge algebra, which is of the so-called soft type. Based on these observations, a novel way to construct critical W_3 strings is given.