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.
Highlights
Functions for a fixed ordering of vertex operators in PS formalism involving 2 massless and 1 massive state and compare them directly with their RNS counterparts
We fix the normalization of the vertex operators of the massive states by comparing same set of 3point functions for a fixed ordering in the two formalisms
After fixing the normalization of the three massive vertex operators by comparing three correlators, we find that the rest of the correlators agree perfectly
Summary
Both minimal as well as the non minimal pure spinor formalisms give the same amplitude prescription at tree level. The tree-level amplitude prescription will be valid for any 3-point functions of open strings states (massive or massless). Step 1: assume a particular order of the vertex operator inserted on the disk and make use of the OPEs between various conformal weight 1 objects to reduce the three point function to a correlation function involving only the three superfields and three pure spinor ghost λα coming from the three vertices. The correlation function V1V2V3 at this stage factorizes completely into two separate correlation functions, one involving Xm fields and the other involving pure spinor fields These can be evaluated independently and their result can be multiplied to obtain the final answer for a given ordering. We found Cadabra to be unparalleled in implementing the algorithm described above
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