On the uniqueness of diffeomorphism symmetry in conformal field theory

DOI10.1007/s00220-005-1335-4zbMath1079.81060arXivmath/0407190OpenAlexW3103258450MaRDI QIDQ2575371

Sebastiano Carpi, Mihály Weiner

Publication date: 9 December 2005

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

Full work available at URL: https://arxiv.org/abs/math/0407190

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) General theory of von Neumann algebras (46L10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

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Cites Work

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• Standard and split inclusions of von Neumann algebras
• Topological sectors and a dichotomy in conformal field theory
• Projective unitary positive-energy representations of \(Diff(S^ 1)\)
• Absence of subsystems for the Haag-Kastler net generated by the energy-momentum tensor in two-dimensional conformal field theory
• Extensions of conformal nets and superselection structures
• Operator algebras and conformal field theory. III: Fusion of positive energy representations of \(LSU(N)\) using bounded operators
• Integrating unitary representations of infinite-dimensional Lie groups
• Operator algebras and conformal field theory
• On the representation theory of Virasoro nets
• Classification of two-dimensional local conformal nets with \(c<1\) and 2-cohomology vanishing for tensor categories
• Classification of local conformal nets. Case \(c < 1\)
• Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions
• The conformal spin and statistics theorem
• Strong additivity and conformal nets
• Time-ordered operator products of sharp-time quadratic forms
• HAAG DUALITY IN CONFORMAL QUANTUM FIELD THEORY
• QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS
• LOCAL NATURE OF COSET MODELS
• Multi-interval subfactors and modularity of representations in conformal field theory