Duality and defects in rational conformal field theory

Fröhlich, Jürg; Fuchs, Jürgen; Runkel, Ingo; Schweigert, Christoph

doi:10.1016/j.nuclphysb.2006.11.017

Cited by 288 publications

(540 citation statements)

References 67 publications

(137 reference statements)

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“…One is the group-like defect and the other, which includes the former, is the duality defect [18,19].…”

Section: Summary and Discussionmentioning

confidence: 99%

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Non-geometric backgrounds based on topological interfaces

Satoh

Sugawara

2015

J. High Energ. Phys.

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Abstract:We study simple models of the world-sheet CFTs describing non-geometric backgrounds based on the topological interfaces, the 'gluing condition' of which imposes T-duality-or analogous twists. To be more specific, we start with the torus partition function on a target spacewith rather general values of radii. The fiber CFT is defined by inserting the twist operators consisting of the topological interfaces which lie along the cycles of the world-sheet torus according to the winding numbers of the base circle. We construct the partition functions involving such duality twists. The modular invariance is achieved straightforwardly, whereas 'unitarization' is generically necessary to maintain the unitarity. We demonstrate it in the case of the equal fiber radii. The resultant models are closely related to the CFTs with the discrete torsion. The unitarization is also physically interpreted as multiple insertions of the twist/interface operators along various directions.

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“…One is the group-like defect and the other, which includes the former, is the duality defect [18,19].…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Note that the zero-mode part G (−) 12;(k 1 ,k 2 ) in (2.18) imposes the 'gluing conditions', 19) whereas those on the oscillator part are…”

Section: Jhep07(2015)022mentioning

confidence: 99%

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Non-geometric backgrounds based on topological interfaces

Satoh

Sugawara

2015

J. High Energ. Phys.

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“…Given the above construction of fields localized to defects, we are now in a position to prove the following partial converse to Theorem 4.1 To prove Theorem 4.4, we take a different approach to evaluating the commutator, [D A , B ] (we can equivalently use the methods in [37]). To that end, consider passing the defect, D A , across the field, B , as in Fig.…”

Section: A Partial Converse Of Theorem 41mentioning

confidence: 99%

Anyonic Chains, Topological Defects, and Conformal Field Theory

Buican

Gromov

2017

Commun. Math. Phys.

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Abstract:Motivated by the three-dimensional topological field theory/two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, which can give rise to an enormously rich (and largely unexplored) space of two-dimensional critical theories in the thermodynamic limit. One remarkable feature of these systems is the appearance of non-local microscopic "topological symmetries" that descend to topological defects of the resulting CFTs. We derive various model-independent properties of these theories and of this topological symmetry/topological defect correspondence. For example, by studying precursors of certain twist and defect fields directly in the anyonic chains, we argue that (under mild assumptions) the two-dimensional CFTs correspond to particular modular invariants with respect to their maximal chiral algebras and that the topological defects descending from topological symmetries commute with these maximal chiral algebras. Using this map, we apply properties of defect Hilbert spaces to show how topological symmetries give a handle on the set of allowed relevant deformations of these theories. Throughout, we give a unified perspective that treats the constraints from discrete symmetries on the same footing as the constraints from topological ones.

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“…The boundary conditions and topological defects have been completely classified in [3] and further studied in [4]. The situation of more general conformal defects is much less clear.…”

Section: Introductionmentioning

confidence: 99%

The reflection coefficient for minimal model conformal defects from perturbation theory

Makabe¹,

Watts²

2018

J. High Energ. Phys.

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We consider a class of conformal defects in Virasoro minimal models that have been defined as fixed points of the renormalisation group and calculate the leading contribution to the reflection coefficient for these defects. This requires several structure constants of the operator algebra of the defect fields, for which we present a derivation in detail. We compare our results with our recent work on conformal defects in the tricritical Ising model.

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Duality and defects in rational conformal field theory

Cited by 288 publications

References 67 publications

Non-geometric backgrounds based on topological interfaces

Non-geometric backgrounds based on topological interfaces

Anyonic Chains, Topological Defects, and Conformal Field Theory

The reflection coefficient for minimal model conformal defects from perturbation theory

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