Spinor Field Realizations of the half-integer $W_{2,s}$ Strings

TL;DR

This paper develops new spinor field realizations of half-integer $W_{2,s}$ strings using the grading BRST method, extending the construction to specific cases of $s=3/2$, 5/2, and 7/2.

Contribution

It introduces novel realizations of half-integer $W_{2,s}$ strings with spinor fields, expanding the algebraic framework for these string models.

Findings

Constructed nilpotent BRST charges for half-integer $W_{2,s}$ strings.

Provided explicit realizations for $s=3/2$, 5/2, 7/2.

Extended the grading BRST method to half-integer $W_{2,s}$ strings.

Abstract

The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct the integer $W_{2,s}$ strings, where the BRST charge is written as $Q_B=Q_0+Q_1$. Using this method, we reconstruct the nilpotent BRST charges $Q_{0}$ for the integer $W_{2,s}$ strings and the half-integer $W_{2,s}$ strings. Then we construct the exact grading BRST charge with spinor fields and give the new realizations of the half-integer $W_{2,s}$ strings for the cases of $s=3/2$, 5/2, and 7/2.