The BRST quantization of the nonlinear $WB_2$ and $W_4$ algebras

TL;DR

This paper constructs the BRST operator for nonlinear $WB_2$ and $W_4$ algebras, revealing a family of solutions with free parameters related to canonical transformations, challenging previous assumptions.

Contribution

It demonstrates that the nilpotent BRST operator for these algebras is not uniquely determined, providing explicit families of solutions with free parameters.

Findings

Found a three-parameter family for $WB_2$

Found a seven-parameter family for $W_4$

Showed free parameters relate to ghost-antighost transformations

Abstract

We construct the BRST operator for the nonlinear $WB_2$ and $W_4$ algebras. Contrary to the general belief, the nilpotent condition of the BRST operator doesn't determine all the coefficients. We find a three and seven parameter family of nilpotent BRST operator for $WB_2$ and $W_4$ respectively. These free parameters are related to the canonical transformation of the ghost antighost fields.