Defining relations for minimal unitary quantum affine W-algebras

DOI10.1007/s00220-023-04902-7arXiv2302.05269OpenAlexW4391519346MaRDI QIDQ6189339

Dražen Adamović, Pierluigi Möseneder Frajria, Victor G. Kac, Paolo Papi

Publication date: 8 February 2024

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

Full work available at URL: https://arxiv.org/abs/2302.05269

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)

Cites Work

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• Characters of (relatively) integrable modules over affine Lie superalgebras
• Quantum reduction and representation theory of superconformal algebras
• VOAs and rank-two instanton SCFTs
• Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture
• \(\hat{\mathfrak sl}(2)_{-\frac{1}{2}}\): a case study
• Determinant formulae and unitarity for the \(N=2\) superconformal algebras in two dimensions or exact results on string compactification
• Lattice construction of logarithmic modules for certain vertex algebras
• Unitary representations of the Virasoro and super-Virasoro algebras
• Superconformal current algebras and their unitary representations
• Details of the non-unitary proof for highest weight representations of the Virasoro algebra
• Virasoro algebras and coset space models
• Vertex operator algebras associated to representations of affine and Virasoro algebras
• Quantum reduction for affine superalgebras
• Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. I: Structural results
• The \(\overline{\text{su}}(2)_{-1/2}\) WZW model and the \(\beta\gamma\) system
• Vertex operator algebras associated to modular invariant representations for \(A_ 1^{(1)}\)
• Integrable modules over affine Lie superalgebras \(\mathfrak{sl}(1|n)^{(1)}\)
• Infinite chiral symmetry in four dimensions
• Admissible-level \(\mathfrak{sl}_3\) minimal models
• Bosonic ghostbusting: the bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• On the semisimplicity of the category \(KL_k\) for affine Lie superalgebras
• Bosonic ghosts at \(c=2\) as a logarithmic CFT
• Conformal embeddings in affine vertex superalgebras
• 3d modularity
• Unitary and non-unitary \(N=2\) minimal models
• Relaxed highest-weight modules. I: Rank 1 cases
• Weight modules over infinite dimensional Weyl algebras
• THE REPRESENTATION THEORY OF THE SO(3) INVARIANT SUPERCONFORMAL ALGEBRA
• From Vertex Operator Algebras to Conformal Nets and Back
• Equivalence between chain categories of representations of affine sl(2) and N=2 superconformal algebras
• On fusion rules and intertwining operators for the Weyl vertex algebra
• Relaxed highest-weight modules II: Classifications for affine vertex algebras
• Invariant Hermitian forms on vertex algebras
• Lie superalgebras
• Vertex algebra approach to fusion rules for \(N=2\) superconformal minimal models
• Unitarity of minimal \(W\)-algebras and their representations. I