Infinite index extensions of local nets and defects

DOI10.1142/S0129055X18500022zbMath1414.81147arXiv1703.03605OpenAlexW3103755253MaRDI QIDQ4603374

Simone Del Vecchio, Luca Giorgetti

Publication date: 20 February 2018

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

Full work available at URL: https://arxiv.org/abs/1703.03605

zbMATH Keywords

conformal field theorysubfactorsHaag-Kastler netsQ-systemsinfinite Jones index

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Applications of operator algebras to the sciences (47L90) Axiomatic quantum field theory; operator algebras (81T05) Subfactors and their classification (46L37)

Related Items

Galois correspondence and Fourier analysis on local discrete subfactors ⋮ A planar algebraic description of conditional expectations ⋮ Conformal covariance and the split property ⋮ Quantum operations on conformal nets ⋮ Wightman fields for two-dimensional conformal field theories with pointed representation category ⋮ Unnamed Item ⋮ Compact hypergroups from discrete subfactors ⋮ Skew-product dynamical systems for crossed product \(C^\ast \)-algebras and their ergodic properties ⋮ Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models

Cites Work

• Unnamed Item
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• Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case
• Scaling algebras for charged fields and short-distance analysis for localizable and topological charges
• Standard and split inclusions of von Neumann algebras
• Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics
• Characterization of crossed product (properly infinite case)
• Endomorphisms of \(C^*\)-algebras, cross products and duality for compact groups
• Index of subfactors and statistics of quantum fields. II: Correspondences, braid group statistics and Jones polynomial
• Restricting positive energy representations of \(\text{Diff}^{+}(S^{1})\) to the stabilizer of \(n\) points
• Structure and classification of superconformal nets
• Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier.
• Extension of Jones' theory on index of arbitrary factors
• Connes' bicentralizer problem and uniqueness of the injective factor of type \(III_ 1\)
• Notes on algebraic invariants for non-commutative dynamical systems
• Finite weight projections in von Neumann algebras
• Relativistic invariance and charge conjugation in quantum field theory
• Some applications of dilatation invariance to structural questions in the theory of local observables
• A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras
• Extensions of conformal nets and superselection structures
• The canonical endomorphism for infinite index inclusions
• Modular structure and duality in conformal quantum field theory
• A duality for Hopf algebras and for subfactors. I
• A new view of the Virasoro algebra
• A theory of dimension
• An analogue of the Kac-Wakimoto formula and black hole conditional entropy
• Conformal subnets and intermediate subfactors
• Subfactor realisation of modular invariants
• On the representation theory of Virasoro nets
• Noncommutative geometry. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 3--9, 2000
• Classification of local conformal nets. Case \(c < 1\)
• Simple injective subfactors
• Minimizing indices of conditional expectations onto a subfactor
• Index of subfactors and statistics of quantum fields. I
• Index for subfactors
• An axiomatization of the lattice of higher relative commutants of a subfactor
• An algebraic spin and statistics theorem
• Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions
• The conformal spin and statistics theorem
• The hypergroupoid of boundary conditions for local quantum observables
• Braided categories of endomorphisms as invariants for local quantum field theories
• Conformal covariance and the split property
• Conformal orbifold theories and braided crossed \(G\)-categories
• Strong additivity and conformal nets
• On intermediate conformal nets
• Fields, observables and gauge transformations. I
• Fields, observables and gauge transformations. II
• Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction
• Algebraic Conformal Quantum Field Theory in Perspective
• Generalized orbifold construction for conformal nets
• MASSLESS SCALAR FREE FIELD IN 1+1 DIMENSIONS I: WEYL ALGEBRAS PRODUCTS AND SUPERSELECTION SECTORS
• Entropy and index for subfactors
• On the duality condition for a Hermitian scalar field
• Algebraic orbifold conformal field theories
• LOCAL FIELDS IN BOUNDARY CONFORMAL QFT
• NETS OF SUBFACTORS
• On the Conjugate Endomorphism in the Infinite Index Case.
• Tensor Categories and Endomorphisms of von Neumann Algebras
• Une classification des facteurs de type ${\rm III}$
• SUPERSELECTION SECTORS WITH BRAID GROUP STATISTICS AND EXCHANGE ALGEBRAS II: GEOMETRIC ASPECTS AND CONFORMAL COVARIANCE
• Remarks on the Type of Von Neumann Algebras of Local Observables in Quantum Field Theory
• The classification of subfactors of index at most 5
• The Classification of Subfactors with Index at Most 5\frac{1}4
• The current algebra on the circle as a germ of local field theories
• Covering group theory for topological groups
• Superselection theory for subsystems.
• Multi-interval subfactors and modularity of representations in conformal field theory
• Phase boundaries in algebraic conformal QFT