Galois currents and the projective kernel in Rational Conformal Field Theory

TL;DR

This paper introduces Galois currents in Rational Conformal Field Theory, classifies theories based on their existence, and describes the projective kernel using computable invariants, advancing understanding of RCFT symmetries.

Contribution

It defines Galois currents, classifies RCFTs accordingly, and characterizes the projective kernel with simple invariants, providing new tools for analyzing RCFT symmetries.

Findings

Theories are classified into two classes based on Galois currents.

The projective kernel is described using easily computable invariants.

Galois currents influence the structure of RCFT symmetries.

Abstract

The notion of Galois currents in Rational Conformal Field Theory is introduced and illustrated on simple examples. This leads to a natural partition of all theories into two classes, depending on the existence of a non-trivial Galois current. As an application, the projective kernel of a RCFT, i.e. the set of all modular transformations represented by scalar multiples of the identity, is described in terms of a small set of easily computable invariants.