Cohomology in the pure spinor formalism for the superstring

A manifestly super-Poincare covariant formalism for the superstring has rec ently been constructed using a pure spinor variable. Unlike the covariant G reen-Schwarz formalism, this new formalism is easily quantized with a BRST operator and tree-level scattering amplitudes have been evaluated in a mani festly covariant manner. In this paper, the cohomology of the BRST operator in the pure spinor formalism is shown to give the usual light-cone Green-S chwarz spectrum. Although the BRST operator does not directly involve the V irasoro constraint, this constraint emerges after expressing the pure spino r variable in terms of SO(8) variables.