Logarithmic intertwining operators and W(2,2p-1)-algebras

Abstract

For every $p\ge 2$, we obtained an explicit construction of a family of $\mathcal{W}(2,2p-1)$-modules, which decompose as direct sum of simple Virasoro algebra modules. Furthermore, we classified all irreducible self-dual $\mathcal{W}(2,2p-1)$-modules, we described their internal structure, and computed their graded dimensions. In addition, we constructed certain hidden logarithmic intertwining operators among two ordinary and one logarithmic $\mathcal{W}(2,2p-1)$-modules. This work, in particular, gives a mathematically precise formulation and interpretation of what physicists have been referring to as "logarithmic conformal field theory" of central charge $c_{p,1}=1-\frac{6(p-1{)}^2}{p},p\ge 2$. Our explicit construction can be easily applied for computations of correlation functions. Techniques from this paper can be used to study the triplet vertex operator algebra $\mathcal{W}(2,(2p-1{)}^3)$ and other logarithmic models.

22 pages; v2: misprints corrected, other minor changes. Final version to appear in Journal of Math. Phys

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Cited by in corpus (28)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• 3d Modularity
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• Generalized twisted modules associated to general automorphisms of a vertex operator algebra
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• A quasi-Hopf algebra for the triplet vertex operator algebra
• The vertex algebras ${\mathcal{R}}^{(p)}$ and ${\mathcal{V}}^{(p)}$
• Modular Transformations and Verlinde Formulae for Logarithmic $(p_{+},p_{-})$-Models
• On ribbon categories for singlet vertex algebras
• Logarithmic intertwining operators and vertex operators
• 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
• Cosets of the ${\mathcal{W}}^k({\mathfrak{sl}}_4,f_{\text{subreg}})$-algebra
• Logarithmic Intertwining Operators and Genus-One Correlation Functions
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}
• Rigid tensor structure on big module categories for some $W$-(super)algebras in type $A$
• On Free Field Realizations of $W(2,2)$-Modules
• On Regularised Quantum Dimensions of the Singlet Vertex Operator Algebra and False Theta Functions
• Fusion rules for the Virasoro algebra of central charge 25
• Free Field Realisations of Staggered Modules in 2D Logarithmic CFTs
• Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity
• Simple weak modules for some subalgebras of the Heisenberg vertex algebra and Whittaker vectors
• Vertex Algebras $\mathcal{W}(p{)}^{A_m}$ and $\mathcal{W}(p{)}^{D_m}$ and Constant Term Identities
• Bimodule structure of the mixed tensor product over $U_{q}s\ell (2|1)$ and quantum walled Brauer algebra
• Logarithmic intertwining operators and the space of conformal blocks over the projective line
• Simple modules for Affine vertex algebras in the minimal nilpotent orbit