Modular Invariance and (Quasi)-Galois symmetry in Conformal Field Theory

TL;DR

This paper explores how Galois and quasi-Galois symmetries can be used to construct modular invariant partition functions in conformal field theory, providing new insights into algebra invariants at specific levels.

Contribution

It introduces the concept of quasi-Galois symmetry and applies it to compute invariants of exceptional algebras at certain levels, advancing the understanding of symmetry in conformal field theory.

Findings

Construction of modular invariant partition functions using Galois symmetry

Introduction of quasi-Galois symmetry as a generalization

Identification of invariants for exceptional algebras at specific levels

Abstract

A brief heuristic explanation is given of recent work with Juergen Fuchs, Beatriz Gato-Rivera and Christoph Schweigert on the construction of modular invariant partition functions from Galois symmetry in conformal field theory. A generalization, which we call quasi-Galois symmetry, is also described. As an application of the latter, the invariants of the exceptional algebras at level $g$ (for example $E_8$ level 30) expected from conformal embeddings are presented. [Contribution to the Proceedings of the International Symposium on the Theory of Elementary Particles Wendisch-Rietz, August 30 - September 3, 1994]