An infinite family of counterexamples to a conjecture on positivity

TL;DR

This paper constructs an infinite family of counterexamples to a conjecture in conformal field theory and tensor category theory, significantly advancing understanding of the conjecture's limitations.

Contribution

It introduces a method to generate an infinite series of counterexamples, extending previous isolated cases and demonstrating the conjecture's failure in a broader context.

Findings

An infinite family of counterexamples is constructed.

The smallest counterexample has order 72.

The results challenge the validity of the conjecture in the field.

Abstract

Recently, G. Mason has produced a counterexample of order 128 to a conjecture in conformal field theory and tensor category theory in [Ma]. Here we easily produce an infinite family of counterexamples, the smallest of which has order 72.