Modular invariants and fusion rule automorphisms from Galois theory

TL;DR

This paper leverages Galois theory of cyclotomic fields to systematically construct modular invariants and fusion rule automorphisms, providing new insights into the structure of exceptional invariants.

Contribution

It introduces a Galois-theoretic approach to generate modular invariants and automorphisms, advancing the understanding of fusion rule symmetries in conformal field theory.

Findings

Constructed integer-valued matrices commuting with the modular S matrix.

Generated automorphisms of fusion rules using Galois theory.

Provided new perspectives on the structure of exceptional invariants.

Abstract

We show that Galois theory of cyclotomic number fields provides a powerful tool to construct systematically integer-valued matrices commuting with the modular matrix S, as well as automorphisms of the fusion rules. Both of these prescriptions allow the construction of modular invariants and offer new insight in the structure of known exceptional invariants.