On Integrable c<1 Open--Closed String Theory

Abstract

The integrable structure of open--closed string theories in the $(p,q)$ conformal minimal model backgrounds is presented. The relation between the $\tau$--function of the closed string theory and that of the open--closed string theory is uncovered. The resulting description of the open--closed string theory is shown to fit very naturally into the framework of the $sl(q,{\rm C})$ KdV hierarchies. In particular, the twisted bosons which underlie and organise the structure of the closed string theory play a similar role here and may be employed to derive loop equations and correlation function recursion relations for the open--closed strings in a simple way.