Boundary ground ring in 2D string theory

The 2D quantum gravity on a disc, or the non-critical theory of open strings, is known to exhibit an integrable structure, the boundary ground ring, which determines completely the boundary correlation functions. Inspired by the recent progress in boundary Liouville theory, we extend the ground ring relations to the case of non-vanishing boundary Liouville interaction known also as FZZT brane in the context of the 2D string theory. The ring relations yield an over-determined set of functional recurrence equations for the boundary correlation functions. The ring action closes on an infinite array of equally spaced FZZT branes for which we propose a matrix model realization. In this matrix model the boundary ground ring is generated by a pair of complex matrix fields. (C) 2004 Elsevier B.V. All rights reserved.