On Principal Admissible Representations and Conformal Field Theory

Abstract

The principal admissible representations of affine Kac-Moody algebras are studied, with a view to their use in conformal field theory. We discuss the generation of the set of principal admissible highest weights, concentrating mainly on $A_r^{(1)}$ at rational level $k$. A related algorithm is described that produces the Malikov-Feigen-Fuchs null vectors of these representations. With the principal admissible description of the highest weights, we are able to prove that field identifications (including maverick ones) lead to the canonical description of the primary fields of the nonunitary diagonal coset theories.

Harvmac (b mode : 32 p; l mode: 36 p), 5 figures, some minor reformulations, references added and typos corrected

References in corpus (4)

• Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level
• $A_1^{(1)}$ Admissible Representations -- Fusion Transformations and Local Correlators
• Fusion rules for admissible representations of affine algebras: the case of $A_2^{(1)}$
• Two-point Functions in Affine Current Algebra and Conjugate Weights

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• sl(2)_{-1/2} and the Triplet Model
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Generating-function method for fusion rules
• Fusion in coset CFT from admissible singular-vector decoupling