Boundary changing operators in the O(n) matrix model

TL;DR

This paper investigates boundary operators in the dense O(n) model on random lattices, deriving their conformal dimensions from matrix models and connecting these results to boundary Liouville theory and loop equations.

Contribution

It provides a new derivation of boundary operator dimensions in the O(n) model using matrix models and links these to boundary Liouville theory.

Findings

Conformal dimensions match regular lattice results.

Established connection between loop equations and boundary Liouville functions.

Extended understanding of boundary operators in random lattice models.

Abstract

We continue the study of boundary operators in the dense O(n) model on the random lattice. The conformal dimension of boundary operators inserted between two JS boundaries of different weight is derived from the matrix model description. Our results are in agreement with the regular lattice findings. A connection is made between the loop equations in the continuum limit and the shift relations of boundary Liouville 3-points functions obtained from Boundary Ground Ring approach.