Implications of an arithmetical symmetry of the commutant for modular invariants

Preprint

8 December 1992

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.hep-th/9212048

Abstract

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3)_k, we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants.

Keywords

COMMUTANT FOR MODULAR
ARITHMETICAL SYMMETRY
MODULAR INVARIANT
CLASSIFICATION
KNOWLEDGE
ALGEBRAS

All Related Versions

Version 1, 1992-12-08, ArXiv
Published version: Nuclear Physics B, 402 (3), 693.

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