Non-invertible topological defects in 4-dimensional $\mathbb {Z}_2$ pure lattice gauge theory

Koide, Masataka; Nagoya, Yuta; Yamaguchi, Satoshi

doi:10.1093/ptep/ptab145

Cited by 73 publications

(52 citation statements)

References 20 publications

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“…When the duality relation is realized via the gauging of the symmetry, the duality symmetry cannot be realized as the ordinary symmetry operation that gives the unitary transformation. Instead, it should be realized as the non-invertible topological defects [24][25][26]. Such an example in 4d QFT was first realized in Ref.…”

Section: Non-invertible Topological Self-duality Defect and Fusion Rulementioning

confidence: 99%

“…Such an example in 4d QFT was first realized in Ref. [24], and later it is noticed that we can systematically define the non-invertible duality symmetry by performing the gauging in the half spacetime [25,26].…”

Section: Non-invertible Topological Self-duality Defect and Fusion Rulementioning

confidence: 99%

“…Even in higher-dimensional and non-topological QFTs, its usefulness has been found out first in the context of the classification of confining string spectra [22,23]. Recently, Koide, Nagoya, and Yamaguchi explicitly constructed the Sduality defect as a non-invertible symmetry for a lattice Z 2 gauge theory [24] by extending the construction of Kramers-Wannier duality defects on the 2d lattice Ising model [9]. A few months later, Refs.…”

Section: Introductionmentioning

confidence: 99%

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Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Hayashi,

Tanizaki

2022

Preprint

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We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U (1) gauge theory with electric and magnetic matters, and it enjoys the SL(2, Z) self-duality at low-energies. SL(2, Z) self-duality does not realize in a naive way, but we notice that the ST p duality transformation becomes the legitimate duality operation by performing the gauging of Z N 1-form symmetry with including the level-p discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a K3 surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.

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Section: Non-invertible Topological Self-duality Defect and Fusion Rulementioning

confidence: 99%

Section: Non-invertible Topological Self-duality Defect and Fusion Rulementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Hayashi,

Tanizaki

2022

Preprint

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“…After a long and prosperous history in spacetime dimensions d " 2, 3 [2][3][4][5][6][7][8][9][10][11][12][13][14], non-invertible symmetries characterized by topological operators satisfying a fusion-algebra (as opposed to a group law), have only very recently been started to be systematically studied in d " 4, especially in nontopological QFTs. The approaches used in [15][16][17] use mixed anomalies and duality defects to construct non-invertible symmetries in 4d gauge theories. In [18] arguments were provided to construct non-invertible defects in Op2q gauge theories by gauging charge conjugation in U p1q gauge theories.…”

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confidence: 99%

Non-Invertible Higher-Categorical Symmetries

Bhardwaj¹,

Bottini²,

Schäfer‐Nameki³

et al. 2022

Preprint

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We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also discuss global fusions of topological defects, where some of the directions of the defects are wrapped along compact sub-manifolds in spacetime while some others are left non-compact, and argue that such a global fusion is described as a local fusion plus a gauging of a higher-categorical symmetry localized along the compact sub-manifold. Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion. We explain how such fusions can be understood in terms of fusion operations of a higher-category, where the dimension does not jump. We also discuss how a 0-form sub-symmetry of a higher-categorical symmetry can be gauged and describe the higher-categorical symmetry of the theory obtained after gauging. This provides a procedure for constructing non-invertible higher-categorical symmetries starting from invertible higher-form or higher-group symmetries and gauging a 0-form symmetry. We illustrate this procedure by constructing non-invertible 2-categorical symmetries in 4d gauge theories and non-invertible 3-categorical symmetries in 5d and 6d theories. We check some of the results obtained using our approach against the results obtained using a recently proposed approach based on 't Hooft anomalies.

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“…) is a counital coassociative coalgebra where ∆ : H → H ⊗ H is the comultiplication and : H → C is the counit. 7 3. The comultiplication ∆ is a unit-preserving algebra homomorphism…”

Section: (H ∆mentioning

confidence: 99%

On lattice models of gapped phases with fusion category symmetries

Inamura

2022

J. High Energ. Phys.

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We construct topological quantum field theories (TQFTs) and commuting projector Hamiltonians for any 1+1d gapped phases with non-anomalous fusion category symmetries, i.e. finite symmetries that admit SPT phases. The construction is based on two-dimensional state sum TQFT whose input datum is an H-simple left H-comodule algebra, where H is a finite dimensional semisimple Hopf algebra. We show that the actions of fusion category symmetries $$ \mathcal{C} $$ C on the boundary conditions of these state sum TQFTs are represented by module categories over $$ \mathcal{C} $$ C . This agrees with the classification of gapped phases with symmetry $$ \mathcal{C} $$ C . We also find that the commuting projector Hamiltonians for these state sum TQFTs have fusion category symmetries at the level of the lattice models and hence provide lattice realizations of gapped phases with fusion category symmetries. As an application, we discuss the edge modes of SPT phases based on these commuting projector Hamiltonians. Finally, we mention that we can extend the construction of topological field theories to the case of anomalous fusion category symmetries by replacing a semisimple Hopf algebra with a semisimple pseudo-unitary connected weak Hopf algebra.

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Non-invertible topological defects in 4-dimensional $\mathbb {Z}_2$ pure lattice gauge theory

Cited by 73 publications

References 20 publications

Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Non-Invertible Higher-Categorical Symmetries

On lattice models of gapped phases with fusion category symmetries

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