Conformal nets III: fusion of defects

Bartels, Arthur; Douglas, Christopher L.; Henriques, André

doi:10.48550/arxiv.1310.8263

Cited by 4 publications

(76 citation statements)

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“…Conformal nets are a mathematical formalization of the notion of conformal field theory [5,6,7,9,10,11,13]. This paper is the fourth in a series investigating coordinate-free conformal nets and their defects [1,2,3]. The notion of coordinatefree conformal nets is a modification of the usual notion of conformal nets, in which one does not demand the positive-energy condition and does not require the existence of a vacuum vector in the vacuum sector.…”

Section: Background and Resultsmentioning

confidence: 99%

“…In the preceding paper [3], we introduced defects between conformal nets and gave examples thereof. (Conjecturally, such defects can also be obtained by taking spatial slices of defects on two-dimensional Minkowski space-time [4].)…”

Section: Background and Resultsmentioning

confidence: 99%

“…In this paper, defects will provide a notion of 1-morphism between conformal nets. Crucially, in [3,Def. 3.1], we introduced the operation of fusion of defects, when the conformal nets have finiteindex-this fusion will provide the composition operation on 1-morphisms between nets.…”

Section: Background and Resultsmentioning

confidence: 99%

“…We also constructed the fundamental interchange isomorphism relating the vertical and horizontal fusion of sectors. All these structures and more are summarized in the first appendix of that paper [3].…”

Section: Background and Resultsmentioning

confidence: 99%

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Conformal nets IV: The 3-category

Bartels,

Douglas,

Henriques

2016

Preprint

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Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. We previously introduced a notion of composition, called fusion, between defects. We also described a notion of sectors between defects, modeling an interaction among or transformation between phase transitions, and defined fusion composition operations for sectors. In this paper we prove that altogether the collection of conformal nets, defects, sectors, and intertwiners, equipped with the fusion of defects and fusion of sectors, forms a symmetric monoidal 3-category. This 3-category encodes the algebraic structure of the possible interactions among conformal field theories. 81T05, 18D05

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Section: Background and Resultsmentioning

confidence: 99%

Section: Background and Resultsmentioning

confidence: 99%

Section: Background and Resultsmentioning

confidence: 99%

Section: Background and Resultsmentioning

confidence: 99%

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Conformal nets IV: The 3-category

Bartels,

Douglas,

Henriques

2016

Preprint

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“…This corresponds to a fusion of the two defects. Fusion of defects have previously been studied in two dimensions [13,14], in supersymmetric theories [15][16][17], and in topological field theories as well as in conformal nets using fusing categories [18][19][20]. In this paper, we will provide three different examples of fusing two defects in four dimensional free theories using the path integral formalism.…”

Section: Introductionmentioning

confidence: 99%

Fusion of conformal defects in four dimensions

Söderberg

2021

Preprint

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We consider two conformal defects close to each other in a free theory, and study what happens as the distance between them goes to zero. This limit is the same as zooming out, and the two defects have fused to another defect. As we zoom in we find a non-conformal effective action for the fused defect. Among other things this means that we cannot in general decompose the two-point correlator of two defects in terms of other conformal defects. We prove the fusion using the path integral formalism by treating the defects as sources for a scalar in the bulk.

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Phase Boundaries in Algebraic Conformal QFT

Bischoff

Kawahigashi

Longo

et al. 2016

Commun. Math. Phys.

117

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Dedicated to Detlev Buchholz on the occasion of his 70th birthday. AbstractWe study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These can be formulated in a common framework originating in Algebraic QFT, with the principle of Einstein Causality playing a prominent role. We classify the phase boundary conditions by the centre of a certain universal construction, which produces a reducible representation in which all possible boundary conditions are realized. For a large class of models, the classification reproduces results obtained in a different approach by Fuchs et al. before.

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Conformal nets III: fusion of defects

Cited by 4 publications

References 0 publications

Conformal nets IV: The 3-category

Conformal nets IV: The 3-category

Fusion of conformal defects in four dimensions

Phase Boundaries in Algebraic Conformal QFT

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