D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries

TL;DR

This paper develops a covariant quantization method for the D=11 superparticle using spinor Lorentz harmonics, revealing connections to pure spinor formalism and suggesting hidden symmetries in D=11 supergravity.

Contribution

It introduces a covariant quantization approach for the D=11 superparticle that links to pure spinor BRST charge and uncovers potential hidden symmetries.

Findings

BRST charge simplifies the superparticle quantization

Cohomology analysis relates to Berkovits pure spinor approach

Hints at hidden SO(16) and E8 symmetries in D=11 supergravity

Abstract

We consider the covariant quantization of the D=11 massless superparticle (M0-brane) in the spinor moving frame or twistor-like Lorentz harmonics formulation. The action involves the set of 16 constrained 32 component Majorana spinors, the spinor Lorentz harmonics parametrizing (as homogeneous coordinates, modulo gauge symmetries) the celestial sphere S9. There presence allows us to separate covariantly the first and the second class constraints of the model. After taking into account the second class constraints by means of Dirac brackets and after further reducing the first class constraints algebra, the system is described in terms of a simple BRST charge associated to the d=1, n=16 supersymmetry algebra. The study of the cohomology of this BRST operator requires a regularization by complexifying the bosonic ghosts for the kappa-symmetry and further reduction of the regularized cohomology problem to the one for a simpler complex BRST charge which is essentially the pure spinor BRST operator by Berkovits, but with a composite pure spinor. This exhibits a possible origin of the complexity (non-hermiticity) characteristic of the Berkovits pure spinor approach. The simple structure of the nontrivial cohomology of the M0-brane BRST charge finds explanation in the properties that the superparticle action exhibits in the so-called `covariantized light-cone' basis. The the covariant quantization in this basis hints possible hidden symmetries of D=11 supergravity. Besides SO(16), we discuss also some indirect arguments in favor of the possible E8 symmetry.