String vertices for the large $N$ limit

Abstract: String vertices of open-closed string field theory on an arbitrary closed string background with $N$ identical D-branes are investigated when $N$ is large. We identify the relevant geometric master equation and solve it using open-closed hyperbolic genus zero string vertices with a milder systolic constraint. The limits corresponding to integrating out open or closed strings are investigated. We highlight the possible implications of our construction to AdS/CFT correspondence.