# Simplified D=11 Pure Spinor b Ghost

## TL;DR

This paper constructs and simplifies a $b$-ghost for the $D=11$ pure spinor superparticle, ensuring it satisfies key BRST relations and introducing a new fermionic vector to streamline the formulation.

## Contribution

It introduces a simplified $b$-ghost for $D=11$ pure spinor superparticle using an $SO(10,1)$ fermionic vector, extending previous $D=10$ methods.

## Key findings

- The $b$-ghost satisfies $oxed{ ext{BRST}}$ relations $oxed{ ext{BRST}}$ triviality.
- Simplification via an $SO(10,1)$ fermionic vector $ar{oldsymbol{ extSigma}}^{i}$.
- The construction generalizes the $D=10$ $b$-ghost to $D=11$.

## Abstract

A $b$-ghost was constructed for the $D=11$ non-minimal pure spinor superparticle by requiring that $\{Q , b\} = T$ where $Q = \Lambda^{\alpha}D_{\alpha} + R^{\alpha}\bar{W}_{\alpha}$ is the usual non-minimal pure spinor BRST operator. As was done for the $D=10$ $b$-ghost, we will show that the $D=11$ $b$-ghost can be simplified by introducing an $SO(10,1)$ fermionic vector $\bar{\Sigma}^{i}$ constructed out of the fermionic spinor $D_{\alpha}$ and pure spinor variables. This simplified version will be shown to satisfy $\{Q, b\} = T$ and $\{b , b\} =$ BRST - trivial.