Conformal Covariance and the Split Property

Morinelli, Vincenzo; Tanimoto, Yoh; Weiner, Mihály

doi:10.1007/s00220-017-2961-3

Cited by 38 publications

(32 citation statements)

References 35 publications

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“…Another important problem raised by the examples in Section 4.2 is which nice properties are expected to be inherited by the dual net, under which conditions. As we have shown that the dual net of a Möbius covariant net in Section 4.2 fails to have the split property, it is a natural question whether the dual nets of Vir c have the split property (if not, they could not be conformally covariant [MTW18]).…”

Section: Open Problemsmentioning

confidence: 99%

Scale and Möbius Covariance in Two-Dimensional Haag–Kastler Net

Morinelli

Tanimoto

2019

Commun. Math. Phys.

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Given a two-dimensional Haag-Kastler net which is Poincaré-dilation covariant with additional properties, we prove that it can be extended to a Möbius covariant net. Additional properties are either a certain condition on modular covariance, or a variant of strong additivity. The proof relies neither on the existence of stress-energy tensor nor any assumption on scaling dimensions. We exhibit some examples of Poincaré-dilation covariant net which cannot be extended to a Möbius covariant net, and discuss the obstructions.

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Section: Open Problemsmentioning

confidence: 99%

Scale and Möbius Covariance in Two-Dimensional Haag–Kastler Net

Morinelli

Tanimoto

2019

Commun. Math. Phys.

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“…Moreover, in order to avoid inconvenient technicalities with disintegration theory, we assume that the starting local extensions have the split property, [DL84]. This assumption is not too restrictive since most interesting models in QFT have this property, in particular all chiral diffeomorphism covariant models [MTW16].…”

Section: Applications To Phase Boundaries In Qftmentioning

confidence: 99%

Infinite index extensions of local nets and defects

Vecchio

Giorgetti

2018

Rev. Math. Phys.

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Subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [LR95] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi, Longo, Popa [ILP98] and Fidaleo, Isola [FI99], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [Lon94] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [BKLR16].Comment: 50 page

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“…A typical appearance of α-induction is an extension of a completely rational local conformal net in the sense of [17, page 498], [16,Definition 8], [20,Definition 3.1]. Note that strong additivity and split property in the definition of complete rationality [16,Definition 8] are unnecessary due to [21] and [22], respectively. Let {A(I) ⊂ B(I)} be such an extension, where I is an interval contained in S 1 .…”

Section: The Relative Drinfeld Commutants Arising From α-Inductionmentioning

confidence: 99%

The Relative Drinfeld Commutant of a Fusion Category and α-Induction

Kawahigashi

2018

International Mathematics Research Notices

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We establish a correspondence among simple objects of the relative commutant of a full fusion subcategory in a larger fusion category in the sense of Drinfeld, irreducible half-braidings of objects in the larger fusion category with respect to the fusion subcategory, and minimal central projections in the relative tube algebra. Based on this, we explicitly compute certain relative Drinfeld commutants of fusion categories arising from α-induction for braided subfactors. We present examples arising from chiral conformal field theory. make analogous computations for the relative commutants of these fusion categories arising from α-induction. Our methods are similar to those in [7] and rely on half-braidings arising from relative braidings studied in [4].We refer the reader to [11] for a general theory of subfactors and to [15] for a review on subfactor theory, category theory, and conformal field theory.

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Conformal Covariance and the Split Property

Cited by 38 publications

References 35 publications

Scale and Möbius Covariance in Two-Dimensional Haag–Kastler Net

Scale and Möbius Covariance in Two-Dimensional Haag–Kastler Net

Infinite index extensions of local nets and defects

The Relative Drinfeld Commutant of a Fusion Category and α-Induction

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