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

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

2004-12-10

arxiv.org/abs/hep-th/0412102v2

J.Phys. A38 (2005) 8259

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0305-4470/38/38/007

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 $\hat{T}$.

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