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

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.

plain LaTeX, 15 pages, no figures. V2- minor changes: misprints corrected, references added, clarifying comments on relation with spinor cohomologies. V3 Shorterned, to appear in Phys.Lett. B

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• N=4 superparticle and super Yang-Mills theory in USp(4) harmonic superspace
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• An analytic superfield formalism for tree superamplitudes in D=10 and D=11
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• Supersymmetric non-Abelian multiwaves in D=3 AdS superspace
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• Hamiltonian approach and quantization of $D=3,\mathcal{N}=1$ supersymmetric non-Abelian multiwave system
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• Multiple M0-brane equations in eleven dimensional pp-wave superspace and BMN matrix model
• Towards the M(atrix) model action in an arbitrary 11D supergravity background. Progress report
• Pure spinors and $D=11$ supergravity
• M(atrix) model interaction with 11D supergravity