Abstract
We provide an alternative compact expression for the 11D pure spinor b-ghost by introducing a new set of negative ghost number operators made out of non-minimal pure spinor variables. Using the algebraic properties satisfied by these operators, it will be straightforwardly shown that \( \left\{Q,b\right\}=\frac{P^2}{2} \), as well as {b, b} = QΩ. As an application of this novel formulation, the ghost number two vertex operator will easily be obtained in a completely covariant manner from a standard descent relation, the ghost number three vertex operator will be shown to satisfy the generalized Siegel gauge condition, and the 11D supergravity two-particle superfield will be constructed in a quite simple way.
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Guillen, M. Taming the 11D pure spinor b-ghost. J. High Energ. Phys. 2023, 135 (2023). https://doi.org/10.1007/JHEP03(2023)135
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DOI: https://doi.org/10.1007/JHEP03(2023)135