BCFT and Ribbon Graphs as tools for open/closed string dualities

In the framework of simplicial models, we construct and we fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analysed from a string theory perspective as tools to deal with open/closed string dualities. Simplicial techniques have being subject of renewed attention since it was clarified that they can play a role in the worldsheet description of open/closed string dualities [1]. In this connection, the hypothesis that the link between SYM gauge and closed string worldsheet dynamics could be explained through the combinatorial data associated to Strebel differentials, suggests that we are undercovering some deep discrete foundation of string dualities, which however is still far from being understood. Aiming to give further insights in this topic, we decided to explore the connection between combinatorial data and string dualities from a more general standpoint. We considered a geometrical set-up in which ribbon graphs are dual to triangulations with localized curvature defects. These provide a natural order parameter which allows to map a N-punctured closed Riemann surface