Simple current symmetries in RCFT

TL;DR

This paper investigates which abelian permutation groups can serve as simple current symmetries in Rational Conformal Field Theory, using weighted permutation actions to classify and illustrate these symmetries.

Contribution

It develops a formalism for classifying simple current symmetries in RCFT via weighted permutation actions and provides classification results with examples.

Findings

Classification of abelian permutation groups as simple current symmetries

Development of a formalism using weighted permutation actions

Illustrative examples of the classification results

Abstract

The question ''Which abelian permutation groups arise as group of simple currents in Rational Conformal Field Theory?'' is investigated using the formalism of weighted permutation actions. After a review of the relevant properties of simple current symmetries, the general theory of WPA-s and admissibility conditions are described, and classification results are illustrated by a couple of examples.