Relating the $b$ ghost and the vertex operators of the pure spinor superstring

TL;DR

This paper computes the operator product expansion between the $b$ ghost and vertex operators in the pure spinor superstring, revealing structural similarities to the bosonic string and clarifying their algebraic relations.

Contribution

It explicitly calculates the OPE between the $b$ ghost and vertex operators, demonstrating their correspondence and the conditions for singularity cancellations in the pure spinor formalism.

Findings

The double pole in the OPE vanishes in Lorentz gauge.

The single pole matches the integrated vertex operator.

The structure aligns with bosonic string results.

Abstract

The OPE between the composite $b$ ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The vanishing of the double pole singularity is Lorentz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.