An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}

Abstract

By extending the methods used in our earlier work, in this paper, we present an explicit realization of logarithmic $\mathcal{W}_{p,p'$}-modules that have L(0) nilpotent rank three. This was achieved by combining the techniques developed in \cite{AdM-2009} with the theory of local systems of vertex operators \cite{LL}. In addition, we also construct a new type of extension of ${\mathcal{W}}_{p,p^{\prime }}$, denoted by $\mathcal{V}$. Our results confirm several claims in the physics literature regarding the structure of projective covers of certain irreducible representations in the principal block. This approach can be applied to other models defined via a pair screenings.

18 pages, v2: one reference added, other minor changes

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Cited by in corpus (5)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• The Verlinde formula in logarithmic CFT
• Modular Transformations and Verlinde Formulae for Logarithmic $(p_{+},p_{-})$-Models
• Fusion and (non)-rigidity of Virasoro Kac modules in logarithmic minimal models at $(p,q)$-central charge
• C-Graded Vertex Algebras and Conformal Flow