Correlation functions in loop models

TL;DR

This paper advances understanding of the O(n) bulk operator algebra in loop models by combining analytical and numerical methods to compute structure constants and analyze the transfer matrix's logarithmic structure, proposing a simplified model for bulk logarithmic CFTs.

Contribution

It provides new computations of structure constants and insights into the logarithmic structure of the O(n) model for generic n, offering a simpler toy model for bulk logarithmic CFTs.

Findings

Computed ratios of structure constants in the O(n) model.

Analyzed the logarithmic structure of the transfer matrix.

Proposed a simplified model for bulk logarithmic CFTs at generic n.

Abstract

In this paper we provide a step towards the understanding of the O($n$) bulk operator algebra. By using a mixture of analytical and numerical methods, we compute (ratios of) structure constants, and analyse the logarithmic structure of the transfer matrix. We believe that the O($n$) model for a generic value of $n = q + q^{-1}$ (i.e. for $q$ not a root of unity) provides a toy model of a bulk logarithmic CFT that is considerably simpler than its counterparts at $q$ a root of unity.