C_2-cofinite W-algebras and their logarithmic representations

Abstract

We discuss our recent results on the representation theory of $\mathcal{W}$--algebras relevant to Logarithmic Conformal Field Theory. First we explain some general constructions of $\mathcal{W}$-algebras coming from screening operators. Then we review the results on $C_2$--cofiniteness, the structure of Zhu's algebras, and the existence of logarithmic modules for triplet vertex algebras. We propose some conjectures and open problems which put the theory of triplet vertex algebras into a broader context. New realizations of logarithmic modules for $\mathcal{W}$-algebras defined via screenings are also presented.

18 pages. To appear in the Proceedings of the Conference on Tensor Categories and Vertex Algebras, Beijing, 2011

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Cited by in corpus (5)

• Quantum SL(2) and logarithmic vertex operator algebras at (p,1)-central charge
• Characterizing braided tensor categories associated to logarithmic vertex operator algebras
• Fusion and (non)-rigidity of Virasoro Kac modules in logarithmic minimal models at $(p,q)$-central charge
• Quasi-lisse extension of affine ${\mathfrak{sl}}_2$ à la Feigin--Tipunin
• ADE subalgebras of the triplet vertex algebra W(p): A-series