Boundary Ground Ring in 2D String Theory

TL;DR

This paper extends the boundary ground ring structure in 2D string theory to include non-zero boundary interactions, deriving functional equations for boundary correlators and proposing a matrix model realization.

Contribution

It introduces the boundary ground ring relations with boundary Liouville interaction and constructs a matrix model for FZZT branes.

Findings

Derived functional recurrence equations for boundary correlators.

Extended the ground ring to non-zero boundary interactions.

Proposed a matrix model realization for FZZT branes.

Abstract

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.