On Discrete Symmetries in su(2) and su(3) Affine Theories and Related Graphs

TL;DR

This paper classifies finite symmetries in su(2) and su(3) affine conformal field theories, linking these symmetries to associated graphs and revealing perfect matches for su(2) and looser matches for su(3).

Contribution

It provides a detailed classification of symmetries in su(2) and su(3) affine theories and explores their correspondence with modular invariant graphs, including the emergence of projective representations.

Findings

Symmetries in su(2) match graph data perfectly.

Symmetries in su(3) match graph data more loosely.

Some graphs lead to projective representations in both cases.

Abstract

We classify the possible finite symmetries of conformal field theories with an affine Lie algebra su(2) and su(3), and discuss the results from the perspective of the graphs associated with the modular invariants. The highlights of the analysis are first, that the symmetries we found in either case are matched by the graph data in a perfect way in the case of su(2), but in a looser way for su(3), and second, that some of the graphs lead naturally to projective representations, both in su(2) and in su(3).