The 11D pure spinor ghost number zero vertex operator

TL;DR

This paper constructs a novel ghost number zero vertex operator in the non-minimal 11D pure spinor formalism, overcoming previous no-go theorems and enabling covariant supergravity amplitude computations.

Contribution

It introduces the first explicit ghost number zero vertex operator in the non-minimal 11D pure spinor framework, with a compact structure and verified descent relations.

Findings

Successfully constructed a ghost number zero vertex operator.

Verified the descent relation with ghost number one vertex.

Reproduced the two-particle superfield through commutator analysis.

Abstract

The 11D pure spinor worldline has been proved to successfully describe the physical states of 11D supergravity in a manifestly super-Poincar\'e covariant fashion. Within this framework, the computation of scattering amplitudes requires the existence of vertex operators carrying different ghost numbers. A recent no-go theorem demonstrated the impossibility of constructing a ghost number zero vertex operator consistent with 11D supergravity in the minimal pure spinor formalism. In this letter, we overcome this obstruction by working in the non-minimal formulation of the 11D pure spinor superparticle. We construct, for the first time, a ghost number zero vertex operator with a remarkably compact structure when expressed in terms of physical operators. We further verify that it satisfies the expected descent relation with the ghost number one vertex operator, and that its commutator with the ghost number three single-particle vertex reproduces the two-particle superfield recently introduced in the literature.