Abstract
We study the cohomology of the massless BRST complex of the Type IIB pure spinor superstring in flat space. In particular, we find that the cohomology at the ghost number three is nontrivial and transforms in the same representation of the supersymmetry algebra as the solutions of the linearized classical supergravity equations. Modulo some finite dimensional spaces, the ghost number three cohomology is the same as the ghost number two cohomology. We also comment on the difference between the naive and semi-relative cohomology, and the role of b-ghost.
Highlights
Vertex operators are one of the central objects in string theory
If the BRST cohomology at the ghost number three is zero any infinitesimal deformation can be continued to a finite deformation, at least as a power series in ε
[8] In [8] we concentrated on the perturbation theory around AdS5 × S5, while in the present paper we work in flat space
Summary
Vertex operators are one of the central objects in string theory. They represent cohomology classes of the BRST operator. It is well known that the physically relevant cohomology problem is the so-called semirelative cohomology [2], which is QBRST acting on the vertex operators V satisfying the following condition: This condition was built-in into the computations of [1]. To defeat the ghost number three cohomology is more difficult It is dangerous as a potential obstacle for continuing an infinitesimal solution to a finite solution (i.e. obstructed deformations of the flat spacetime). We do not have such a proof in the pure spinor formalism It follows from the consistency of [6] that there is no obstacle in extending the infinitesimal deformation to higher orders. It would be good to have a transparent proof of this fact using the language of BRST cohomology and vertex operators This would probably require the use of the composite b-ghost
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