The level 2 and 3 modular invariants for the orthogonal algebras

1998/09/04 by Terry Gannon, Gannon, Terry
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical functions and polynomials #Quantum Algebra (math.QA) #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.math/9809020

18 pages, plain tex

arxiv created 1998/09/04 · openalex publication_date 1998/09/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper finds for all orthogonal algebras (i.e. the B and D series) all modular invariant 1-loop partition functions at levels 1,2,3. Previously, only those at level 1 were classified. An extraordinary number of exceptionals appear at level 2 -- indeed this is the primary motivation for this paper -- and we find infinitely many new ones there. The only level 3 exceptionals occur for B₂ and D₇, and the latter appear to be new. The B_2,3 and D_7,3 exceptionals are cousins of the "E₆" and "E₈" exceptionals in the A-D-E classification for affine A₁, while the level 2 exceptionals are related to the lattice invariants of affine u(1).

Related

• The Classification of SU(3) Modular Invariants Revisited
• Kac-Peterson, Perron-Frobenius, and the Classification of Conformal Field Theories
• Modular Invariance and (Quasi)-Galois symmetry in Conformal Field Theory
• Modular Invariance of Characters for Affine Lie Algebras at Subprincipal Admissible Levels
• An Observation on Finite Groups and WZW Modular Invariants