Impurity Operators in RSOS Models

TL;DR

This paper constructs impurity operators in RSOS models using algebraic analysis, linking physical insertions with mathematical intertwiners, and verifies their correspondence through perturbation theory.

Contribution

It introduces a novel construction of impurity operators in RSOS models and establishes their mathematical representation via intertwiners of quantum affine algebra modules.

Findings

Impurity operators are represented as half-infinite insertions of fusion-RSOS Boltzmann weights.

A detailed perturbation theory confirms the correspondence between physical and mathematical descriptions.

The construction generalizes the face analogue of higher spin line insertions in vertex models.

Abstract

We give a construction of impurity operators in the `algebraic analysis' picture of RSOS models. Physically, these operators are half-infinite insertions of certain fusion-RSOS Boltzmann weights. They are the face analogue of insertions of higher spin lines in vertex models. Mathematically, they are given in terms of intertwiners of $U(\hat{sl}_2)_q$ modules. We present a detailed perturbation theory check of the conjectural correspondence between the physical and mathematical constructions in a particular simple example.