Higher Coxeter graphs associated to affine su(3) modular invariants

Abstract

The affine $su(3)$ modular invariant partition functions in 2d RCFT are associated with a set of generalized Coxeter graphs. These partition functions fall into two classes, the block-diagonal (Type I) and the non block-diagonal (Type II) cases, associated, from spectral properties, to the subsets of subgroup and module graphs respectively. We introduce a modular operator $\hat{T}$ taking values on the set of vertices of the subgroup graphs. It allows us to obtain easily the associated Type I partition functions. We also show that all Type II partition functions are obtained by the action of suitable twists $\vartheta$ on the set of vertices of the subgroup graphs. These twists have to preserve the values of the modular operator $\hat{T}$.

Version 2. Abstract, introduction and conclusion rewritten, references added. 36 pages

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Cited by in corpus (8)

• Comments about quantum symmetries of SU(3) graphs
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• Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus
• Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings
• Exceptional quantum subgroups for the rank two Lie algebras B2 and G2
• Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
• From modular invariants to graphs: the modular splitting method