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

TL;DR

This paper explores a novel BRST charge in open string field theory that naturally excludes GSO-odd states in RNS superstrings, aligning with pure spinor constraints without requiring GSO-projection.

Contribution

It introduces a new nilpotent BRST operator that automatically removes GSO-odd states and deforms on-shell constraints consistent with pure spinor formalism.

Findings

GSO-odd spectrum is automatically cut off

GSO-even spectrum remains intact

Deformed on-shell constraints match pure spinor formalism

Abstract

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