A BRST charge for non-critical $\W_{2,s}$ strings

TL;DR

This paper constructs BRST charges for non-critical $ ext{W}_{2,s}$ strings, demonstrating their existence for certain algebraic structures derived from quantum $ ext{W}_{2,s}$ algebras, advancing understanding of string theory symmetries.

Contribution

It provides a general method to construct BRST charges for non-critical $ ext{W}_{2,s}$ strings, expanding the algebraic framework of string theory.

Findings

BRST charges constructed for $ ext{W}_{2,4}$, $ ext{W}_{2,5}$, $ ext{W}_{2,6}$, and $ ext{W}_{2,8}$ strings

Existence of BRST charges for soft-type algebras from two copies of quantum $ ext{W}_{2,s}$ algebras

Supports the algebraic consistency of non-critical $ ext{W}_{2,s}$ string theories

Abstract

We present a general argument for the construction of BRST charges of the `non-critical' $\W_{2,4}$, $\W_{2,5}$, $\W_{2,6}$, and $\W_{2,8}$ strings. This evidences the existence of BRST charges for a kind of soft-type algebras which can be constructed from two copies of quantum $\W_{2,s}$ algebras, (s=3,4,5,6,8).