Non-unitary conformal field theory and logarithmic operators for disordered systems

DOI10.1016/S0550-3213(97)00014-XzbMath0925.81328arXivhep-th/9605062MaRDI QIDQ675914

Juan-Miguel Gracia

Publication date: 12 March 1997

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

Full work available at URL: https://arxiv.org/abs/hep-th/9605062

zbMATH Keywords

current algebra approachDirac modelGaussian disordered systemsKnizhnik Zamolodchikov equationsrandom bond Ising modelsuperalgebra approach

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65)

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Cites Work

• Unnamed Item
• Unnamed Item
• Current algebras and Wess-Zumino model in two dimensions
• Two-dimensional conformal field theory for disordered systems at criticality
• Logarithmic operators and hidden continuous symmetry in critical disordered models
• Logarithmic operators in conformal field theory
• FUSION AND TENSORING OF CONFORMAL FIELD THEORY AND COMPOSITE FERMION PICTURE OF FRACTIONAL QUANTUM HALL EFFECT
• ON MODULAR INVARIANT PARTITION FUNCTIONS OF CONFORMAL FIELD THEORIES WITH LOGARITHMIC OPERATORS
• KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS
• The tensor product of two irreducible representations of the spl(2,1) superalgebra
• Irreducible representations of the osp(2,1) and spl(2,1) graded Lie algebras
• Lie superalgebras