Tensor categories arising from the Virasoro algebra

DOI10.1016/j.aim.2021.107601zbMath1477.17084arXiv2002.03180OpenAlexW3126075013MaRDI QIDQ2227291

Thomas Creutzig, Florencia Orosz Hunziker, David Ridout, Jin-Wei Yang, Cuipo (Cuibo) Jiang

Publication date: 15 February 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.03180

zbMATH Keywords

Virasoro algebranon \(C_2\) vertex tensor categoryuniversal Virasoro vertex algebrasvertex tensor categories

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Vertex operators; vertex operator algebras and related structures (17B69) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Fusion categories, modular tensor categories, modular functors (18M20) Braided monoidal categories and ribbon categories (18M15)

Related Items (15)

Correspondences among CFTs with different W-algebra symmetry ⋮ Correspondences of categories for subregular \(\mathcal{W}\)-algebras and principal \(\mathcal{W}\)-superalgebras ⋮ Direct limit completions of vertex tensor categories ⋮ Uprolling unrolled quantum groups ⋮ The vertex algebras \(\mathcal{R}^{(p)}\) and \(\mathcal{V}^{(p)}\) ⋮ An \(\mathfrak{sl}_2\)-type tensor category for the Virasoro algebra at central charge 25 and applications ⋮ Rigid tensor structure on big module categories for some \(W\)-(super)algebras in type \(A\) ⋮ Ribbon tensor structure on the full representation categories of the singlet vertex algebras ⋮ On ribbon categories for singlet vertex algebras ⋮ Tensor categories of affine Lie algebras beyond admissible levels ⋮ The quantum group dual of the first-row subcategory for the generic Virasoro VOA ⋮ Trialities of orthosymplectic \(\mathcal{W} \)-algebras ⋮ Admissible-level \(\mathfrak{sl}_3\) minimal models ⋮ Urod algebras and Translation of W-algebras ⋮ On the representation theory of the vertex algebra L−5/2(sl(4))

Cites Work

• Coset constructions of logarithmic \((1, p)\) models
• Vertex algebras associated to modified regular representations of the Virasoro algebra
• From percolation to logarithmic conformal field theory
• Logarithmic intertwining operators and associative algebras
• On complete reducibility for infinite-dimensional Lie algebras
• Singular vectors of the \(N=1\) superconformal algebra.
• Braided tensor categories related to \(\mathcal{B}_p\) vertex algebras
• Classical and quantum conformal field theory
• \(\hat{\mathfrak sl}(2)_{-\frac{1}{2}}\): a case study
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory
• Kazhdan-Lusztig correspondence for the representation category of the triplet \(W\)-algebra in logarithmic CFT
• Virasoro algebras and coset space models
• Vertex operator algebras associated to representations of affine and Virasoro algebras
• Some finiteness properties of regular vertex operator algebras
• Determining fusion rules by \(A(V)\)-modules and bimodules
• On the structure of Verma modules over Virasoro and Neveu-Schwarz algebras
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra.
• Degenerate conformal field theories and explicit expressions for some null vectors
• Braided tensor categories of admissible modules for affine Lie algebras
• W-algebras for Argyres-Douglas theories
• Cosets, characters and fusion for admissible-level \(\mathfrak{osp}(1 | 2)\) minimal models
• Fusion categories for affine vertex algebras at admissible levels
• Logarithmic link invariants of \(\overline{U}_q^H(\mathfrak{sl}_2)\) and asymptotic dimensions of singlet vertex algebras
• A construction of admissible \(A_1^{(1)}\)-modules of level \(-\frac{4}{3}\)
• Fusion rings for degenerate minimal models.
• On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
• A theory of tensor products for module categories for a vertex operator algebra. III
• A theory of tensor products for module categories for a vertex operator algebra. IV
• A theory of tensor products for module categories for a vertex operator algebra. I
• A theory of tensor products for module categories for a vertex operator algebra. II
• Logarithmic operators in conformal field theory
• Intertwining operator algebras and vertex tensor categories for affine Lie algebras
• S-duality for the large \(N = 4\) superconformal algebra
• Indecomposable fusion products
• On the tensor structure of modules for compact orbifold vertex operator algebras
• Vertex algebras for S-duality
• On ribbon categories for singlet vertex algebras
• False theta functions and the Verlinde formula
• Quantum Langlands dualities of boundary conditions, \(D\)-modules, and conformal blocks
• Schur-Weyl duality for Heisenberg cosets
• \(W\)-algebras as coset vertex algebras
• Braided tensor categories and extensions of vertex operator algebras
• Associative-algebraic approach to logarithmic conformal field theories
• Modular transformations and Verlinde formulae for logarithmic (\(p_+,p_-\))-models
• On the triplet vertex algebra \(\mathcal W(p)\)
• The vertex algebras \(\mathcal{R}^{(p)}\) and \(\mathcal{V}^{(p)}\)
• ON MODULAR INVARIANT PARTITION FUNCTIONS OF CONFORMAL FIELD THEORIES WITH LOGARITHMIC OPERATORS
• The tensor structure on the representation category of the $\mathcal {W}_p$ triplet algebra
• Logarithmic conformal field theory: beyond an introduction
• Tensor Structures Arising from Affine Lie Algebras. I
• NGK and HLZ: Fusion for Physicists and Mathematicians
• Virasoro representations and fusion for general augmented minimal models
• A LOGARITHMIC GENERALIZATION OF TENSOR PRODUCT THEORY FOR MODULES FOR A VERTEX OPERATOR ALGEBRA
• Logarithmic intertwining operators and W(2,2p−1) algebras
• On staggered indecomposable Virasoro modules
• RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES
• Tensor Structures Arising from Affine Lie Algebras. III
• Tensor Structures Arising from Affine Lie Algebras. IV
• BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY
• AN ALGEBRAIC APPROACH TO LOGARITHMIC CONFORMAL FIELD THEORY
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• Quantum $q$-Langlands Correspondence
• Representation theory of $L_k(\mathfrak {osp}(1 \vert 2))$ from vertex tensor categories and Jacobi forms
• On infinite order simple current extensions of vertex operator algebras
• QUASI-RATIONAL FUSION PRODUCTS
• Logarithmic minimal models
• Direct limit completions of vertex tensor categories
• A quasi-Hopf algebra for the triplet vertex operator algebra
• From Jack polynomials to minimal model spectra
• Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules
• C 1-Cofiniteness and Fusion Products for Vertex Operator Algebras
• On axiomatic approaches to vertex operator algebras and modules
• Introduction to quantum groups
• Modular-invariance of trace functions in orbifold theory and generalized Moonshine.
• Boundary algebras and Kac modules for logarithmic minimal models
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