Simplified D=11 Pure Spinor b Ghost

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.