Boundary operators in minimal Liouville gravity and matrix models

TL;DR

This paper explores the relationship between matrix boundary operators in minimal Liouville gravity and matrix models, revealing how they create matter boundary conditions and establishing recursion relations among boundary correlators.

Contribution

It provides a new interpretation of matrix boundary operators as FZZT branes and extends the analysis to two matrix models, connecting matrix correlators with Liouville boundary functions.

Findings

Matrix boundary operators create boundaries with Cardy matter states.

Recursion relations among boundary correlators are established.

Comparison between matrix model correlators and Liouville boundary functions confirms the correspondence.

Abstract

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.