Boundary correlation numbers in one matrix model

TL;DR

This paper introduces a multi-flavor vector coupled matrix model that reproduces boundary correlation numbers in 2D minimal Liouville gravity, extending the loop operator approach to various boundary conditions.

Contribution

It presents a novel matrix model framework that captures boundary correlation functions in 2D gravity, generalizing previous methods to multi-flavor scenarios.

Findings

Two-flavor model reproduces boundary two-point functions.

Model describes non-trivial boundary conditions for matter and Liouville fields.

Proposes n-flavor model for multiple boundary conditions.

Abstract

We introduce one matrix model coupled to multi-flavor vectors. The two-flavor vector model is demonstrated to reproduce the two-point correlation numbers of boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity on disk, generalizing the loop operator (resolvent) description. The model can properly describe non-trivial boundary conditions for the matter Cardy state as well as for the Liouville field. From this we propose that the n-flavor vector model will be suited for producing the boundary correlation numbers with n different boundary conditions on disk.