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Using an elementary perturbative open string field theory solution involvinga twistor-like parameter, we study the cohomology of new nilpotent BRST chargecorresponding to the space-time background defined by this solution. The BRSTcohomology of the deformed background automatically cuts off the GSO-oddspectrum in RNS superstring theory and keeps the GSO-even spectrum intact,without a need of GSO-projection. The on-shell constraints in the GSO-evensector get deformed in the new background, corresponding to BRST typetransformations of the low-energy effective action with the ghost-likecommuting spinor parameter satisfying the pure spinor constraint in $d=10$.

A Note on GSO-Free RNS Superstrings and Pure Spinor Constraint