Equivalence of the 11D pure spinor and Brink-Schwarz-like superparticle cohomologies

Abstract

The D=11 pure spinor formulation of the superparticle allows a simple realization of covariant quantization, unlike the D=11 Brink-Schwarz-like superparticle. We explicitly show the equivalence between the cohomologies of these two models in the context of two different group decompositions: SO(10,1)→SO(1,1)×SO(9) and SO(10,1)→SO(3,1)×SO(7). We also carry out a light-cone analysis of the pure spinor cohomology and show that it correctly reproduces the SO(9) equations of motion for D=11 linearized supergravity.