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hal-00003510, version 2

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

D. Hammaoui 1, G. Schieber () 1, 2, E.H. Tahri 1

Résumé : 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 $\hat{T}$.

  • 1 :  Laboratoire de Physique Théorique et des Particules (LPTP)
  • Université Mohamed I
  • 2 :  Centro Brasileiro de Pesquisas Físicas (CBPF)
  • Ministério da Ciência e Tecnologia
  • Domaine : Physique/Physique des Hautes Energies - Théorie
    Physique/Physique mathématique
  • Mots-clés : conformal field theory – modular invariance – Higher Coxeter systems – fusion algebra
  • Commentaire : Version 2. Abstract – introduction and conclusion rewritten – references added. 36 pages.
  • Versions disponibles :  v1 (10-12-2004) v2 (06-05-2005)
 
  • hal-00003510, version 2
  • http://hal.archives-ouvertes.fr/hal-00003510
  • oai:hal.archives-ouvertes.fr:hal-00003510
  • Contributeur : Gil Schieber <>
  • Soumis le : Jeudi 5 Mai 2005, 22:12:03
  • Dernière modification le : Vendredi 6 Mai 2005, 08:59:02