sl^(2)_{-1/2}: A Case Study

Abstract

The construction of the non-logarithmic conformal field theory based on sl^(2)_{-1/2} is revisited. Without resorting to free-field methods, the determination of the spectrum and fusion rules is streamlined and the beta gamma ghost system is carefully derived as the extended algebra generated by the unique finite-order simple current. A brief discussion of modular invariance is given and the Verlinde formula is explicitly verified.

33 pages, 2 figures v2: added refs and clarifying comments

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Cited by in corpus (41)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
• Modular Data and Verlinde Formulae for Fractional Level WZW Models II
• Coset Constructions of Logarithmic (1,p)-Models
• 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
• Macdonald Index and Chiral Algebra
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• sl(2)_{-1/2} and the Triplet Model
• Relaxed highest-weight modules I: rank $1$ cases
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• Relaxed singular vectors, Jack symmetric functions and fractional level $\widehat{\mathfrak{sl}}(2)$ models
• The Verlinde formula in logarithmic CFT
• Superspace conformal field theory
• Modular Transformations and Verlinde Formulae for Logarithmic $(p_{+},p_{-})$-Models
• Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models
• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Modularity of logarithmic parafermion vertex algebras
• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• Surface defects, flavored modular differential equations and modularity
• Unitary and non-unitary $N=2$ minimal models
• Fusion rules for the logarithmic $N=1$ superconformal minimal models II: including the Ramond sector
• Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector
• Admissible-level ${\mathfrak{sl}}_3$ minimal models
• W-Algebras Extending Affine gl(1|1)
• Rigid tensor structure on big module categories for some $W$-(super)algebras in type $A$
• Deformation quantizations from vertex operator algebras
• On modular properties of the AdS3 CFT
• Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras
• On the structure of W-algebras in type A
• Duality structures for module categories of vertex operator algebras and the Feigin Fuchs boson
• Quasi-Characters in $\widehat{su(2)}$ Current Algebra at Fractional Levels
• Staggered modules of $N=2$ superconformal minimal models
• Staggered and affine Kac modules over $A_1^{(1)}$
• Strings and D-branes in curved space-time
• Bosonic Ghost Correlators: A Case Study
• Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras
• Simple modules for Affine vertex algebras in the minimal nilpotent orbit