On the Classification of Diagonal Coset Modular Invariants

TL;DR

This paper classifies all modular invariant partition functions for specific diagonal coset models, revealing many new invariants and relating their modular matrices to those of WZNW tensor products.

Contribution

It introduces a novel relation between modular matrices of GKO diagonal cosets and WZNW tensor products, enabling comprehensive classification of invariants.

Findings

Classified all invariants for $su(3)_kigoplus su(3)_1/su(3)_{k+1}$ for all k.

Classified all invariants for $su(2)_kigoplus su(2)_\ell/su(2)_{k+\ell}$ for all k and infinitely many \\ell.

Discovered many new invariants previously unknown.

Abstract

We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3)_k\oplus su(3)_1/su(3)_{k+1}$ for all positive integer level $k$, and $su(2)_k\oplus su(2)_\ell/su(2)_{k+\ell}$ for all $k$ and infinitely many $\ell$ (in fact, for each $k$ a positive density of $\ell$). Of all these classifications, only that for $su(2)_k\oplus su(2)_1/su(2)_{k+1}$ had been known. Our lists include many new invariants.