Boundary fields and renormalization group flow in the two-matrix model

TL;DR

This paper uses matrix model techniques to analyze the Ising model on a random surface with a boundary magnetic field, calculating key physical quantities and interpreting the results as a renormalization group flow between boundary conditions.

Contribution

It provides exact calculations of disk amplitude, boundary magnetization, and bulk magnetization in the presence of a boundary field within the two-matrix model framework.

Findings

Exact solutions for boundary and bulk magnetizations.

Identification of RG flow from non-conformal to conformal boundary conditions.

Connection to boundary RG flows in flat space theories.

Abstract

We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary field. The results of these calculations can be interpreted in terms of renormalization group flow induced by the boundary operator. In the continuum limit this RG flow corresponds to the flow from non-conformal to conformal boundary conditions which has recently been studied in flat space theories.