Under open/closed string duality: What do the external closed string momenta get mapped to in the multi-loop open string amplitude?

Question

The open/closed string duality implies that a planar multi-loop open string amplitude gets mapped to a tree-level closed string one. Please correct me if I am wrong, but under a conformal transformation each of the boundaries of the open string worldsheet should become a vertex operator for an external closed string state, right? Considering now the reverse logic, i.e., if to a generic closed string tree amplitude we perform the inverse conformal transformation above such that it now looks a multi-loop open string diagram, what do the closed string momenta corresponds to in the open string multiloop picture?

Answer 1

It seems your question is answered in Chapter 5 of this lecture notes.