Amplitudes involving massive states using pure spinor formalism

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.