General properties of vertices with two Ramond or twisted states

Abstract

We construct the generator U(γ) of a projective transformation γ both in the Ramond and twisted sectors. The projective group structure implies a number of nontrivial relations involving determinants and inverses of infinite-dimensional matrices. Using those relations we show the factorization properties of a newly constructed vertex, that allows for emission of spin fields, by sewing together two R-R-NS vertices through a R leg and recovering a vertex with 2 R and 2 NS legs. This procedure is extended to the case of a vertex for a scalar theory involving twisted and untwisted states.