Modular data and Verlinde formulae for fractional level WZW models. II

DOI10.1016/j.nuclphysb.2013.07.008zbMath1282.81158arXiv1306.4388OpenAlexW4229762597MaRDI QIDQ2438249

Thomas Creutzig, David Ridout

Publication date: 10 March 2014

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.4388

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (62)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fusion in fractional level \(\widehat{\mathfrak sl}(2)\)-theories with \(k=-\frac{1}{2}\)
• Operator content of two-dimensional conformally invariant theories
• \(\hat{\mathfrak sl}(2)_{-1/2}\) and the triplet model
• Conformal field theory
• Fusion rules and modular transformations in 2D conformal field theory
• Logarithmic lift of the \(\widehat{\text{su}}(2)_{-1/2}\) model
• The \(\text{GL}(1| 1)\) WZW-model: from supergeometry to logarithmic CFT
• The extended algebra of the \(\text SU(2)\) Wess-Zumino-Witten models
• Two projections of singular vectors of Verma modules over the affine Lie algebra \(A^1_1\)
• \(\hat{\mathfrak sl}(2)_{-\frac{1}{2}}\): a case study
• Structure of representations with highest weight of infinite-dimensional Lie algebras
• The relation between quantum \(W\) algebras and Lie algebras
• Singular vectors of \(W\) algebras via DS reduction of \(A^{(1)}_{2}\)
• Quantum reduction for affine superalgebras
• Resolutions and characters of irreducible representations of the \(N=2\) superconformal algebra
• On principal admissible representations and conformal field theory
• Fusion and singular vectors in \(A_ 1^{(1)}\) highest weight cyclic modules
• Singular vectors in Verma modules over Kac-Moody algebras
• The \(\overline{\text{su}}(2)_{-1/2}\) WZW model and the \(\beta\gamma\) system
• Vertex operator algebras associated to modular invariant representations for \(A_ 1^{(1)}\)
• Modular data and Verlinde formulae for fractional level WZW models I
• Relating the archetypes of logarithmic conformal field theory
• Strings in AdS3 and the SL(2,R) WZW model. I: The spectrum
• Logarithmic conformal field theory: beyond an introduction
• On staggered indecomposable Virasoro modules
• Fusion rules and boundary conditions in thec= 0 triplet model
• Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
• AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
• THE ANNIHILATING IDEALS OF MINIMAL MODELS
• Equivalence between chain categories of representations of affine sl(2) and N=2 superconformal algebras
• Modular invariance of characters of vertex operator algebras
• Takiff superalgebras and conformal field theory
• The mock modular data of a family of superalgebras
• Fusion rules and logarithmic representations of a WZW model at fractional level

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