Fractional-Level Kac-Moody Algebras and Nonunitary Coset Conformal Theories

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概要

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• In the coset construction, the admissible representations of Kac-Moody algebras at fractional level give rise to nonunitary conformal field theories. We simplify the description (due to Kac and Wakimoto) of the possible highest weights of admissible representations. For every subgroup of the centre of a finite Lie algebra, we find an infinite sequence of modular invariant combinations of characters of admissible representations. Products of our invariants provide a large class of partition functions (and therefore the spectra) of nonunitary coset models. Under an assumption (proved valid for su(2) and su(3)) we give a formula for the fusion rules of untwisted affine algebras at fractional level, in terms of those at integer level and the affine outer automorphisms. We also find a more general formula expressing them in terms of the affine Weyl group and integer-level fusion rules. These formulae determine the fusion rules for nonunitary coset models. Finally, a suggestive linear relation is found between the modular S matrices for the fractional level su(N) algebras and those for the corresponding (nonunitary) W_N minimal models.

• 理論物理学刊行会の論文
• 1991-03-29

著者

• WALTON M.

  Department of Experimental Psychology

• Mathieu P

  Fao

• MATHIEU P.

  Department de physique, University Laval

• Walton M.

  Department De Physique University Laval : Department Of Physics University Of Lethbridge

• Walton M.A.

  Department de physique, University Laval

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