Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach

TL;DR

This paper investigates the covariant BRST quantization of the D=11 superparticle using spinor moving frames, revealing the intrinsic complexity of Berkovits's pure spinor approach through a detailed analysis of constraints and cohomology.

Contribution

It provides a covariant quantization framework for the M0-brane that clarifies the origin of the pure spinor complexity in superparticle models.

Findings

The complexification of bosonic ghosts is necessary for cohomology calculation.

The resulting BRST charge resembles Berkovits's pure spinor operator with a composite pure spinor.

The approach separates first and second class constraints covariantly.

Abstract

To exhibit the possible origin of the inner complexity of the Berkovits's pure spinor approach, we consider the covariant BRST quantization of the D=11 massless superparticle (M0-brane) in its spinor moving frame or twistor-like Lorentz harmonics formulation. The presence of additional twistor-like variables (spinor harmonics) allows us to separate covariantly the first and the second class constraints. After taking into account the second class constraints by means of Dirac brackets and after further reducing the first class constraints algebra, the dynamical system is described by the cohomology of a simple BRST charge associated to the d=1, n=16 supersymmetry algebra. The calculation of the cohomology of this BRST operator requires a regularization which implies the complexification of the bosonic ghost associated to the kappa-symmetry and further leads to a complex (non-Hermitian) BRST charge which is essentially the `pure spinor' BRST operator by Berkovits, but with a composite pure spinor.