Domain Walls Between 3d Phases of Reshetikhin–Turaev TQFTs

Koppen, Vincent; Mulevicius, Vincentas; Runkel, Ingo; Schweigert, Christoph

doi:10.1007/s00220-022-04489-5

Cited by 4 publications

(1 citation statement)

References 39 publications

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“…Along the worldvolume Σ, this appears to be a gauged

(k-p)

‐form symmetry, obtained as a ‘condensation’ of the k ‐form symmetry defects on the codimension p submanifold. Such a gauging is described as a higher gauging or as p ‐gauging the k ‐form symmetry, see also [12–25] for other discussions. The resulting theory along Σ, obtained by gauging the restriction of the higher‐form symmetry, is a condensation defect.…”

Section: Introductionmentioning

confidence: 99%

Decomposition, Condensation Defects, and Fusion

Robbins

Sharpe

2022

Fortschritte der Physik

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In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay with notions of decomposition, the statement that d-dimensional quantum field theories with global (d − 1)-form symmetries are equivalent to disjoint unions of other quantum field theories. We will also construct new (sometimes non-invertible) defects, and compute their fusion products, again utilizing decomposition. An important role will be played in all these analyses by theta angles for gauged higher-form symmetries, which can be used to select individual universes in a decomposition.

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“…Along the worldvolume Σ, this appears to be a gauged

(k-p)

Section: Introductionmentioning

confidence: 99%

Decomposition, Condensation Defects, and Fusion

Robbins

Sharpe

2022

Fortschritte der Physik

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Reshetikhin–Turaev TQFTs Close Under Generalised Orbifolds

Carqueville,

Mulevičius,

Runkel

et al. 2024

Commun. Math. Phys.

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We specialise the construction of orbifold graph TQFTs introduced in Carqueville et al. (Orbifold graph TQFTs) to Reshetikhin–Turaev defect TQFTs. We explain that the modular fusion category $$\mathcal {C}_\mathcal {A}$$ C A constructed in Mulevičius and Runkel (Quant Topol 13(3):459–523, 2023. https://doi.org/10.4171/QT/170) from an orbifold datum $$\mathcal {A}$$ A in a given modular fusion category $$\mathcal {C}$$ C is a special case of the Wilson line ribbon categories introduced as part of the general theory of orbifold graph TQFTs. Using this, we prove that the Reshetikhin–Turaev TQFT obtained from $$\mathcal {C}_\mathcal {A}$$ C A is equivalent to the orbifold of the TQFT for $$\mathcal {C}$$ C with respect to the orbifold datum $$\mathcal {A}$$ A .

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Orbifolds of Topological Quantum Field Theories

Carqueville

2024

Reference Module in Materials Science and Materials Engineering

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Domain Walls Between 3d Phases of Reshetikhin–Turaev TQFTs

Cited by 4 publications

References 39 publications

Decomposition, Condensation Defects, and Fusion

Decomposition, Condensation Defects, and Fusion

Reshetikhin–Turaev TQFTs Close Under Generalised Orbifolds

Orbifolds of Topological Quantum Field Theories

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