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

J.Phys. A38 (2005) 8259 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 prop...

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Bibliographic Details
Main Authors Hammaoui, D, Schieber, G, Tahri, E. H
Format Journal Article
LanguageEnglish
Published 10.12.2004
Subjects
Mathematics - Mathematical Physics
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
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Summary:J.Phys. A38 (2005) 8259 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 $\hat{T}$.
DOI:10.48550/arxiv.hep-th/0412102