Amplitudes Involving Massive States Using Pure Spinor Formalism

TL;DR

This paper verifies the equivalence of pure spinor and RNS formalisms for superstring amplitudes involving first massive states, extending previous results known for massless states.

Contribution

It provides the first explicit computation of massless-massless-massive 3-point functions in pure spinor formalism and confirms their agreement with RNS results.

Findings

Exact match of 3-point functions for massive states between formalisms

Normalization of vertex operators fixed by comparison

Extension of equivalence from massless to massive states

Abstract

Same amplitudes evaluated independently using RNS and pure spinor formalism are expected to agree. While for massless states, this fact has been firmly established, for massive states such an explicit check has been lacking so far. We compute all massless-massless-massive 3-point functions in open supertrings in pure spinor formalism for the first massive states and compare them with the corresponding RNS results. We fix the normalization of the vertex operators of the massive states by comparing same set of 3-point functions for a fixed ordering in the two formalisms. Once fixed, the subsequent 3-point functions for each inequivalent ordering match exactly. This extends the explicit demonstration of equivalence of pure spinor and RNS formalism from massless states to first massive states.