Boundary operators in the O(n) and RSOS matrix models

TL;DR

This paper investigates a new boundary condition in the O(n) model using matrix models, deriving boundary operator spectra and linking it to RSOS model boundary conditions through diagrammatic and loop equation analysis.

Contribution

It introduces a novel boundary condition in the O(n) model and establishes a detailed correspondence with RSOS model boundary conditions.

Findings

Boundary operators and conformal weights are explicitly computed.

A correspondence between O(n) and RSOS boundary conditions is established.

The approach combines matrix model techniques with loop equations.

Abstract

We study the new boundary condition of the O(n) model proposed by Jacobsen and Saleur using the matrix model. The spectrum of boundary operators and their conformal weights are obtained by solving the loop equations. Using the diagrammatic expansion of the matrix model as well as the loop equations, we make an explicit correspondence between the new boundary condition of the O(n) model and the "alternating height" boundary conditions in RSOS model.