Critical and non-critical W_{2,4} strings

TL;DR

This paper constructs a generalized BRST operator for non-critical W_{2,4} strings, analyzes its cohomology, and explores the physical spectra of related higher-spin string theories, advancing understanding of non-critical higher-spin string models.

Contribution

It introduces a generalized BRST operator for non-critical W_{2,4} strings and analyzes the cohomology and spectra of higher-spin W_{2,s} string theories.

Findings

Complete cohomology of critical W_{2,4} BRST operator obtained

Physical spectra of s=5 and s=6 string theories investigated

Generalized BRST operator links matter and gravity in non-critical W_{2,4} strings

Abstract

Nilpotent BRST operators for higher-spin $W_{2,s}$ strings, with currents of spins 2 and $s$, have recently been constructed for $s=4$, 5 and 6. In the case of $W_{2,4}$, this operator can be understood as being the BRST operator for the critical $W\!B_2$ string. In this paper, we construct a generalised BRST operator that can be associated with a non-critical $W_{2,4}$ string, in which $W\!B_2$ matter is coupled to the $W\!B_2$ gravity of the critical case. We also obtain the complete cohomology of the critical $W_{2,4}$ BRST operator, and investigate the physical spectra of the $s=5$ and $s=6$ string theories.