The Classification of Affine SU(3) Modular Invariant Partition Functions
Terry Gannon
TL;DR
This paper provides a complete classification of SU(3) affine Lie algebra modular invariant partition functions, extending the known classifications and proposing a method applicable to other affine algebras.
Contribution
It offers the first full classification of SU(3) modular invariant partition functions and introduces a new approach that can be applied to other affine Lie algebras.
Findings
Complete classification of SU(3) invariants achieved
Method applicable to other affine Lie algebras
Preliminary work on SU(2) invariants included
Abstract
A complete classification of the WZNW modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of SU(2), and level 1 of all simple algebras. In this paper we solve the classification problem for SU(3) modular invariant partition functions. Our approach will also be applicable to other affine Lie algebras, and we include some preliminary work in that direction, including a sketch of a new proof for SU(2).
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