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Automorphism modular invariants of current algebras

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Abstract

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 untwisted affine Lie 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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Author notes

  1. P. Ruelle (Chercheur Qualifié FNRS)

    Present address: Institut de Physique Théorique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

Authors and Affiliations

  1. Mathematics Department, Concordia University, H3G 1M8, Montréal, Canada

    T. Gannon

  2. Departamento de Física de Partículas, Universidade de Santiago, E-15706, Santiago de Compostela, Spain

    P. Ruelle (Chercheur Qualifié FNRS)

  3. Physics Department, University of Lethbridge, T1K 3M4, Lethbridge, Alberta, Canada

    M. A. Walton

Authors
  1. T. Gannon
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  2. P. Ruelle
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  3. M. A. Walton
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Additional information

Communicated by R.H. Dijkgraaf

Supported in part by NSERC.

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Gannon, T., Ruelle, P. & Walton, M.A. Automorphism modular invariants of current algebras. Commun.Math. Phys. 179, 121–156 (1996). https://doi.org/10.1007/BF02103717

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