New Spinor Field Realizations of the Non-Critical $W_{3}$ String

TL;DR

This paper introduces new spinor field realizations of the non-critical $W_{3}$ algebra by linearizing it with a spin-1 current, enabling the construction of BRST charges for the $W_{3}$ string.

Contribution

It presents novel spinor realizations of the $W_{3}$ algebra that facilitate the formulation of BRST charges in non-critical $W_{3}$ string theory.

Findings

New spinor realizations of $W_{3}$ algebra derived

Construction of nilpotent BRST charges for non-critical $W_{3}$ string

Linearization of $W_{3}$ algebra using a spin-1 current

Abstract

We investigate the new spinor field realizations of the $W_{3}$ algebra, making use of the fact that the $W_{3}$ algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi-Rouet-Stora--Tyutin (BRST) charges of the spinor non-critical $W_{3}$ string.