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

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.Comment: 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.

String-Like Description of Gravity and Possible Applications for F-theory

The Lorentz harmonic formulation of D-dimensional bosonic p-brane theory with $D\geq (p+1)(p+2)/2$ coupled to an antisymmetric tensor field of rank d=(p+1) provides the dynamical ground for the description of d=(p+1) dimensional Gravity. It hence realizes the idea of Regge and Teitelboim on a 'string-like' description of gravity. The simplest nontrivial models of such a kind are provided by free D-dimensional p-branes in which world volumes are embedded as minimal surfaces. Possible applications of such a model with d=2+2 and D=2+10 for studying a geometry of bosonic sector of F-theory are considered. Some speculations inspired by the proposed model are presented.Comment: 11 pages. LATE