Automorphism Modular Invariants of Current Algebras

Details Automorphism Modular Invariants of Current Algebras Automorphism Modular Invariants of Current Algebras

1995-03-21

arxiv.org/abs/hep-th/9503141v1

Commun.Math.Phys. 179 (1996) 121-156

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, plain TeX

Scientific paper

10.1007/BF02103717

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac--Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.

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