Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras

Abstract

The ${\mathcal{B}}_p$-algebras are a family of vertex operator algebras parameterized by $p\in {\mathbb{Z}}_{\ge 2}$. They are important examples of logarithmic CFTs and appear as chiral algebras of type $(A_1,A_{2p-3})$ Argyres-Douglas theories. The first member of this series, the ${\mathcal{B}}_2$-algebra, are the well-known symplectic bosons also often called the $\beta \gamma$ vertex operator algebra. We study categories related to the ${\mathcal{B}}_p$ vertex operator algebras using their conjectural relation to unrolled restricted quantum groups of ${\mathfrak{sl}}_2$. These categories are braided, rigid and non semi-simple tensor categories. We list their simple and projective objects, their tensor products and their Hopf links. The latter are successfully compared to modular data of characters thus confirming a proposed Verlinde formula of David Ridout and the second author.

44 pages

References in corpus (47)

• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Infinite Chiral Symmetry in Four Dimensions
• New N=2 Superconformal Field Theories in Four Dimensions
• Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center
• Study of $N=2$ Superconformal Field Theories in $4$ Dimensions
• Vertex operator algebras, the Verlinde conjecture and modular tensor categories
• On the Superconformal Index of Argyres-Douglas Theories
• Logarithmic Conformal Field Theory: Beyond an Introduction
• Fusion rules and logarithmic representations of a WZW model at fractional level
• Braided tensor categories and extensions of vertex operator algebras
• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
• Surface Defects and Chiral Algebras
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Schur-Weyl Duality for Heisenberg Cosets
• Modular Data and Verlinde Formulae for Fractional Level WZW Models II
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• Vertex Operator Algebras and 3d N=4 gauge theories
• Coset Constructions of Logarithmic (1,p)-Models
• The tensor structure on the representation category of the ${\mathcal{W}}_p$ triplet algebra
• N=1 Lagrangians for generalized Argyres-Douglas theories
• Logarithmic intertwining operators and W(2,2p-1)-algebras
• Simple current extensions beyond semi-simplicity
• Some remarks on the unrolled quantum group of sl(2)
• sl^(2)_{-1/2}: A Case Study
• Conformal Manifolds in Four Dimensions and Chiral Algebras
• Braided tensor categories of admissible modules for affine Lie algebras
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• On Irregular Singularity Wave Functions and Superconformal Indices
• Fusion in Fractional Level sl^(2)-Theories with k=-1/2
• N=2 S-duality Revisited
• Bosonic Ghosts at $c=2$ as a Logarithmic CFT
• sl(2)_{-1/2} and the Triplet Model
• RG flows with supersymmetry enhancement and geometric engineering
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories
• The Verlinde formula in logarithmic CFT
• Surface Defect Indices and 2d-4d BPS States
• Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models
• SL(2,Z)-action for ribbon quasi-Hopf algebras
• ODE/IM correspondence and the Argyres-Douglas theory
• On the chiral algebra of Argyres-Douglas theories and S-duality
• Modularity of logarithmic parafermion vertex algebras
• Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• Unitary and non-unitary $N=2$ minimal models
• Logarithmic conformal field theories of type $B_n,\ell =4$ and symplectic fermions

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• Duality of subregular W-algebras and principal W-superalgebras
• A slow review of the AGT correspondence
• The vertex algebras ${\mathcal{R}}^{(p)}$ and ${\mathcal{V}}^{(p)}$
• On ribbon categories for singlet vertex algebras
• Tensor categories of affine Lie algebras beyond admissible levels
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• Direct limit completions of vertex tensor categories
• Tensor structure on the Kazhdan-Lusztig category for affine $\mathfrak{gl}(1|1)$
• Ribbon tensor structure on the full representation categories of the singlet vertex algebras
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Subregular W-algebras of type A
• Rigid tensor structure on big module categories for some $W$-(super)algebras in type $A$
• On the structure of W-algebras in type A
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity
• $N=1$ super Virasoro tensor categories
• Feigin-Semikhatov conjecture and related topics