Correspondences of categories for subregular \(\mathcal{W}\)-algebras and principal \(\mathcal{W}\)-superalgebras

DOI10.1007/s00220-021-04297-3OpenAlexW4281760202MaRDI QIDQ2147975

Yanyan Li

Publication date: 21 June 2022

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.00942

Mathematics Subject Classification ID

Quantum field theory; related classical field theories (81Txx) Groups and algebras in quantum theory (81Rxx) Lie algebras and Lie superalgebras (17Bxx) Category theory; homological algebra (18-XX)

Related Items (4)

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 ⋮ Subregular W-algebras of type A ⋮ Trialities of orthosymplectic \(\mathcal{W} \)-algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rationality of Bershadsky-Polyakov vertex algebras
• Coset constructions of logarithmic \((1, p)\) models
• Quantization of the Drinfel'd-Sokolov reduction.
• The FZZ duality with boundary
• Rationality of \(W\)-algebras: principal nilpotent cases
• Monoidal supercategories
• Quantum reduction and representation theory of superconformal algebras
• Irreducible characters of general linear superalgebra and super duality
• Super duality and irreducible characters of ortho-symplectic Lie superalgebras
• Vertex algebras at the corner
• Conformal field theory
• On quantum Galois theory
• Braided tensor categories related to \(\mathcal{B}_p\) vertex algebras
• \(W_n^{(n)}\) algebras
• Finite vs affine \(W\)-algebras
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory
• Simple WZW currents
• Vertex operator algebras associated to representations of affine and Virasoro algebras
• Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction
• Regularity of rational vertex operator algebras
• Quantum reduction for affine superalgebras
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra.
• Introduction to vertex operator algebras and their representations
• Resolutions and characters of irreducible representations of the \(N=2\) superconformal algebra
• Braided tensor categories of admissible modules for affine Lie algebras
• W-algebras for Argyres-Douglas theories
• Realizations of simple affine vertex algebras and their modules: the cases \({\widehat{sl(2)}}\) and \({\widehat{osp(1,2)}}\)
• Fusion categories for affine vertex algebras at admissible levels
• A construction of admissible \(A_1^{(1)}\)-modules of level \(-\frac{4}{3}\)
• Higher-level Appell functions, modular transformations, and characters
• On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
• A characterization of vertex algebras associated to even lattices
• 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. I
• A theory of tensor products for module categories for a vertex operator algebra. II
• S-duality for the large \(N = 4\) superconformal algebra
• Duality of subregular \(\mathcal{W} \)-algebras and principal \(\mathcal{W} \)-superalgebras
• Higher rank FZZ-dualities
• Tensor categories of affine Lie algebras beyond admissible levels
• Kazama-Suzuki coset construction and its inverse
• Gluing vertex algebras
• Bosonic ghostbusting: the bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• Trialities of \(\mathcal{W} \)-algebras
• Screening operators and parabolic inductions for affine \(\mathcal{W}\)-algebras
• Cohomological Hall algebras, vertex algebras and instantons
• Vertex algebras for S-duality
• Tensor categories arising from the Virasoro algebra
• On ribbon categories for singlet vertex algebras
• Localization of affine \(W\)-algebras
• Liouville correlation functions from four-dimensional gauge theories
• Quantum Langlands dualities of boundary conditions, \(D\)-modules, and conformal blocks
• Schur-Weyl duality for Heisenberg cosets
• Modularity of relatively rational vertex algebras and fusion rules of principal affine \(W\)-algebras
• Unitary and non-unitary \(N=2\) minimal models
• \(W\)-algebras as coset vertex algebras
• \(C_2\)-cofiniteness of cyclic-orbifold models
• Braided tensor categories and extensions of vertex operator algebras
• Cosets of Bershadsky-Polyakov algebras and rational \({\mathcal W}\)-algebras of type \(A\)
• Modular data and Verlinde formulae for fractional level WZW models. II
• Level-rank duality via tensor categories
• The vertex algebras \(\mathcal{R}^{(p)}\) and \(\mathcal{V}^{(p)}\)
• Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, II
• W-Algebras Extending $$\widehat{\mathfrak{g}\mathfrak{l}}(1\vert 1)$$
• Lattice Subalgebras of Strongly Regular Vertex Operator Algebras
• On the superconformal index of Argyres–Douglas theories
• Parafermion vertex operator algebras and $W$-algebras
• Integrability of C2-cofinite vertex operator algebras
• Associated Varieties of Modules Over Kac-Moody Algebras and C2-Cofiniteness of W-Algebras
• Logarithmic intertwining operators and W(2,2p−1) algebras
• Semi-infinite cohomology and string theory
• Quantum $q$-Langlands Correspondence
• The irreducible modules and fusion rules for the parafermion vertex operator algebras
• Cosets of the 𝒲^{𝓀}(𝔰𝔩₄,𝔣_{𝔰𝔲𝔟𝔯𝔢𝔤})-algebra
• A sufficient condition for convergence and extension property for strongly graded vertex algebras
• Equivalence between chain categories of representations of affine sl(2) and N=2 superconformal algebras
• Modular Invariant Representations of the Superconformal Algebra
• N = 4 Superconformal Algebras and Diagonal Cosets
• Simple Current Extensions of Tensor Products of Vertex Operator Algebras
• Direct limit completions of vertex tensor categories
• Simple current extensions beyond semi-simplicity
• Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules
• Tensor Categories
• DIFFERENTIAL EQUATIONS AND INTERTWINING OPERATORS
• Introduction to Lie Algebras and Representation Theory
• Urod algebras and Translation of W-algebras
• Lie superalgebras
• Vertex algebra approach to fusion rules for \(N=2\) superconformal minimal models

This page was built for publication: Correspondences of categories for subregular \(\mathcal{W}\)-algebras and principal \(\mathcal{W}\)-superalgebras