Nilpotency of the b ghost in the non-minimal pure spinor formalism

TL;DR

This paper proves the nilpotency of the b ghost in the non-minimal pure spinor formalism without relying on previous invalid assumptions, clarifying its fundamental properties.

Contribution

It establishes the nilpotency of the b ghost without the earlier restrictive assumptions, advancing the understanding of the formalism's consistency.

Findings

Proves nilpotency of the b ghost without previous assumptions

Clarifies the fundamental nature of the b ghost

Strengthens the theoretical foundation of the pure spinor formalism

Abstract

The b ghost in the non minimal pure spinor formalism is not a fundamental field. It is based on a complicated chain of operators and proving its nilpotency is nontrivial. Chandia proved this property in arXiv:1008.1778, but with an assumption on the non-minimal variables that is not valid in general. In this work, the b ghost is demonstrated to be nilpotent without this assumption.