sl(2)_{-1/2} and the Triplet Model

Abstract

Conformal field theories with sl(2)_{-1/2} symmetry are studied with a view to investigating logarithmic structures. Applying the parafermionic coset construction to the non-logarithmic theory, a part of the structure of the triplet model is uncovered. In particular, the coset theory is shown to admit the triplet W-algebra as a chiral algebra. This motivates the introduction of an augmented sl(2)_{-1/2}-theory for which the corresponding coset theory is precisely the triplet model. This augmentation is envisaged to lead to a precise characterisation of the "logarithmic lift" of the non-logarithmic sl(2)_{-1/2}-theory that has been proposed by Lesage et al.

27 pages, 3 figures, 1 table; v2 added refs to vertex algebra literature and a few comments

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Cited by in corpus (32)

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• Schur-Weyl Duality for Heisenberg Cosets
• Modular Data and Verlinde Formulae for Fractional Level WZW Models II
• Coset Constructions of Logarithmic (1,p)-Models
• The tensor structure on the representation category of the ${\mathcal{W}}_p$ triplet algebra
• Simple current extensions beyond semi-simplicity
• Strings on ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• Braided tensor categories of admissible modules for affine Lie algebras
• Fusion in Fractional Level sl^(2)-Theories with k=-1/2
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• A modular invariant bulk theory for the c=0 triplet model
• Relaxed highest-weight modules I: rank $1$ cases
• Relaxed singular vectors, Jack symmetric functions and fractional level $\widehat{\mathfrak{sl}}(2)$ models
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• Modularity of logarithmic parafermion vertex algebras
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
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• Factorization of correlations in two-dimensional percolation on the plane and torus
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• A commutant realization of Odake's algebra