Boundary operators in the one-matrix model

TL;DR

This paper develops a comprehensive method to construct all boundary operators in the one-matrix model, connecting matrix model results with Liouville gravity boundary correlators and ground ring operators.

Contribution

It introduces a systematic construction of all boundary operators in the one-matrix model, extending previous work limited to a single operator, and links these to continuum Liouville boundary theories.

Findings

Reproduces Liouville boundary 2-point functions from matrix model correlators.

Establishes a connection between matrix model relations and boundary ground ring operators.

Provides a complete set of boundary operators for the one-matrix model.

Abstract

The one matrix model is known to reproduce in the continuum limit the (2,2p+1) minimal Liouville gravity. Recently, two of the authors have shown how to construct arbitrary critical boundary conditions within this matrix model. So far, between two such boundary conditions only one boundary operator was constructed. In this paper, we explain how to construct all the set of boundary operators that can be inserted. As a consistency check, we reproduce the corresponding Liouville boundary 2pt function from the matrix model correlator. In addition, we remark a connection between a matrix model relation and the boundary ground ring operator insertion in the continuum theory.