The Classification of Affine SU(3) Modular Invariant Partition Functions

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).

30 pages, (plain tex)

References in corpus (2)

• WZW Commutants, Lattices, and Level 1 Partition Functions
• Partition Functions for Heterotic WZW Conformal Field Theories

Cited by in corpus (44)

• Symmetries and Strings of Adjoint QCD${}_2$
• Orbifold groupoids
• Boundary Conditions in Rational Conformal Field Theories
• Comments on nonunitary conformal field theories
• From CFT's to Graphs
• Galois Modular Invariants of WZW Models
• Conformal Field Theory, Tensor Categories and Operator Algebras
• Strange Metals in One Spatial Dimension
• Poincaré Series, 3d Gravity and Averages of Rational CFT
• Automorphism Modular Invariants of Current Algebras
• Graphs and Reflection Groups
• Simple-current algebra constructions of 2+1D topological orders
• Towards a Classification of su(2)$⨁\cdots ⨁$su(2) Modular Invariant Partition Functions
• On the Classification of Diagonal Coset Modular Invariants
• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
• Comments about quantum symmetries of SU(3) graphs
• SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants
• From conformal embeddings to quantum symmetries: an exceptional SU(4) example
• Fusion rules of modular invariants
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• Subfactors and Mathematical Physics
• AdS${}_3$ Gravity and RCFT Ensembles with Multiple Invariants
• The fully packed loop model as a non-rational $W_3$ conformal field theory
• Chiral Primaries in Strange Metals
• Modular invariants and fusion rule automorphisms from Galois theory
• Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus
• Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory
• Determination of quantum symmetries for higher ADE systems from the modular T matrix
• The W_N minimal model classification
• On the mass-coupling relation of multi-scale quantum integrable models
• Lectures on conformal field theory and Kac-Moody algebras
• Cloning SO(N) level 2
• The level 2 and 3 modular invariants of SU(n)
• Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras
• Exceptional quantum subgroups for the rank two Lie algebras B2 and G2
• Classification of ${\mathfrak{sl}}_3$ relations in the Witt group of nondegenerate braided fusion categories
• On parity functions in conformal field theories
• Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)
• Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
• Torus structure on graphs and twisted partition functions for minimal and affine models
• Fixed points and fusion rings. Part 1
• Galois Relations on Knot Invariants
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• RG flow between $W_3$ minimal models by perturbation and domain wall approaches