The level 2 and 3 modular invariants of SU(n)

TL;DR

This paper classifies all modular invariant partition functions for su(n) at levels 2 and 3, extending known results from level 1 and identifying new exceptional cases related to rank-level duality.

Contribution

It provides the first explicit classification of modular invariants for su(n) at levels 2 and 3, including new exceptional cases and their relation to rank-level duality.

Findings

Identified all level 2 and 3 modular invariants for su(n).

Discovered a new exceptional invariant at level 3 for n=5.

Confirmed existing invariants are related by rank-level duality.

Abstract

In this paper we explicitly classify all modular invariant partition functions for su(n) at level 2 and 3. Previously, these were known only for level 1. The level 2 exceptionals exist at n=10, 16, and 28; the level 3 exceptionals exist at n=5, 9, and 21. One of these is new, but the others were all anticipated by the "rank-level duality" relating su(n) level k and su(k) level n. The main recent result which this paper rests on is the classification of "ADE_7-type invariants".