Spinor field realizations of the non-critical $W_{2,4}$ string based on the linear $W_{1,2,4}$ algebra

TL;DR

This paper constructs spinor field realizations of the non-critical $W_{2,4}$ algebra by linearizing it with a spin-1 current and develops corresponding nilpotent BRST charges for the string theory.

Contribution

It introduces a novel method to realize the $W_{2,4}$ algebra using spinor fields and constructs the associated BRST charges for non-critical string models.

Findings

Successfully linearized the $W_{2,4}$ algebra with a spin-1 current.

Built nilpotent BRST charges based on these realizations.

Provided a framework for non-critical $W_{2,4}$ string analysis.

Abstract

In this paper, we investigate the spinor field realizations of the $W_{2,4}$ algebra, making use of the fact that the $W_{2,4}$ algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical $W_{2,4}$ string were built with these realizations.