Decoupling of unphysical states in the minimal pure spinor formalism II

TL;DR

This paper provides a proof that unphysical states decouple in the minimal pure spinor superstring formalism at any genus, addressing issues with picture changing operators not being BRST closed.

Contribution

It offers a new proof of decoupling of unphysical states in the minimal pure spinor formalism, accounting for non-BRST-closed picture changing operators.

Findings

Decoupling of unphysical states holds at arbitrary genus.

Invariance of the path integral measure is crucial for the proof.

Addresses issues with picture changing operators in the formalism.

Abstract

This is the second of a series of two papers where decoupling of unphysical states in the minimal pure spinor formalism is investigated. The multi-loop amplitude prescription for the minimal pure spinor superstring formulated in hep-th/0406055 involves the insertion of picture changing operators in the path integral. In the first paper it was shown that these operators are not BRST closed inside correlators. Therefore a new proof of decoupling of BRST exact states is needed. In this paper we present such a proof, which applies to arbitrary genus. It relies in part on a (previously unnoticed) invariance of the path integral measure.