An obstruction to subfactor principal graphs from the graph planar algebra embedding theorem

TL;DR

This paper introduces a new obstruction criterion for subfactor principal graphs, demonstrating that most in a certain family must contain a cycle by depth 6, except for the Haagerup subfactor.

Contribution

It establishes a novel obstruction based on graph cycles, advancing the classification of subfactor principal graphs.

Findings

Most 3-supertransitive principal graphs in the family contain a cycle by depth 6

The Haagerup subfactor principal graph is the only exception

Provides a new tool for subfactor graph classification

Abstract

We find a new obstruction to the principal graphs of subfactors. It shows that in a certain family of 3-supertransitive principal graphs, there must be a cycle by depth 6, with one exception, the principal graph of the Haagerup subfactor.