Unifying constructions of non-invertible symmetries

Bhardwaj, Lakshya; Schäfer-Nameki, Sakura; Tiwari, Apoorv

doi:10.21468/scipostphys.15.3.122

Cited by 29 publications

(36 citation statements)

References 58 publications

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“…along with fusion rules 2 symmetric QFT T carrying this 2-charge, which is a problem that is left for future work. The authors think that such 2-charges could be produced by coupling 2d Ising CFT to T judiciously, probably in a similar way to the construction of theta topological defects discussed in [26,46,47], but now extending the construction to include non-topological defects.…”

Section: Example 26: Symmetry Fractionalization To Ising Categorymentioning

confidence: 95%

“…that arises whenever we have (p) symmetry in a d-dimensional QFT. See [17] for more details on higher-categories associated to symmetries, and [46] or the end of appendix B for more details on the higher-categories (11) associated to invertible symmetries. The elements of this (d − 1)-category include both symmetry generators and condensation defects.…”

Section: Condensation Defectsmentioning

confidence: 99%

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Generalized charges, part I: Invertible symmetries and higher representations

Bhardwaj,

Schäfer-Nameki

2024

SciPost Phys.

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qq-charges describe the possible actions of a generalized symmetry on qq-dimensional operators. In Part I of this series of papers, we describe qq-charges for invertible symmetries; while the discussion of qq-charges for non-invertible symmetries is the topic of Part II. We argue that qq-charges of a standard global symmetry, also known as a 0-form symmetry, correspond to the so-called (q+1)(q+1)-representations of the 0-form symmetry group, which are natural higher-categorical generalizations of the standard notion of representations of a group. This generalizes already our understanding of possible charges under a 0-form symmetry! Just like local operators form representations of the 0-form symmetry group, higher-dimensional extended operators form higher-representations. This statement has a straightforward generalization to other invertible symmetries: qq-charges of higher-form and higher-group symmetries are (q+1)(q+1)-representations of the corresponding higher-groups. There is a natural extension to higher-charges of non-genuine operators (i.e. operators that are attached to higher-dimensional operators), which will be shown to be intertwiners of higher-representations. This brings into play the higher-categorical structure of higher-representations. We also discuss higher-charges of twisted sector operators (i.e. operators that appear at the boundary of topological operators of one dimension higher), including operators that appear at the boundary of condensation defects.

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Section: Example 26: Symmetry Fractionalization To Ising Categorymentioning

confidence: 95%

Section: Condensation Defectsmentioning

confidence: 99%

Generalized charges, part I: Invertible symmetries and higher representations

Bhardwaj,

Schäfer-Nameki

2024

SciPost Phys.

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“…There is a multitude of realizations now. Most relevant for the field theoretic approach that was the focus in this paper are the following constructions, which have direct 3d realizations [46][47][48][49][50][51][52][53][54]. Non-invertible symmetries in 3d are of course very well explored in the context of modular tensor categories, however here the interesting question is related to the interplay between non-invertible symmetries and superconformal symmetry in 3d.…”

Section: Introductionmentioning

confidence: 99%

Generalized symmetries and anomalies of 3d $\mathcal{N}=4$ SCFTs

Bhardwaj,

Bullimore,

Ferrari

et al. 2024

SciPost Phys.

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We study generalized global symmetries and their ’t Hooft anomalies in 3d \mathcal{N}=4𝒩=4 superconformal field theories (SCFTs). Following some general considerations, we focus on good quiver gauge theories, comprised of balanced unitary nodes and unbalanced unitary and special unitary nodes. While the global form of the Higgs branch symmetry group may be determined from the UV Lagrangian, the global form of Coulomb branch symmetry groups and associated mixed ’t Hooft anomalies are more subtle due to potential symmetry enhancement in the IR. We describe how Coulomb branch symmetry groups and their mixed ’t Hooft anomalies can be deduced from the UV Lagrangian by studying center charges of various types of monopole operators, providing a concrete and unambiguous way to implement ’t Hooft anomaly matching. The final expression for the symmetry group and ’t Hooft anomalies has a concise form that can be easily read off from the quiver data, specifically from the positions of the unbalanced and flavor nodes with respect to the positions of the balanced nodes. We provide consistency checks by applying our method to compute symmetry groups of 3d \mathcal{N}=4𝒩=4 theories corresponding to magnetic quivers of 4d Class S theories and 5d SCFTs. We are able to match these results against the flavor symmetry groups of the 4d and 5d theories computed using independent methods. Another strong consistency check is provided by comparing symmetry groups and anomalies of two theories related by 3d mirror symmetry.

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“…Concomitantly, rational CFTs played a prominent role in the discovery and characterization of topological defects, leading to novel forms of global symmetry, and the development of alternative descriptions in terms of higher dimensional topological field theories (TQFT) (see e.g. [12][13][14][15][16][17][18][19][20][21][22][23][24]). In this work, we will focus on the former aspect, namely the description of interesting global symmetry structures and the exploration of their consequences.…”

Section: Introductionmentioning

confidence: 99%

Exploring duality symmetries, multicriticality and RG flows at c = 2

Damia,

Galati,

Hulik

et al. 2024

J. High Energ. Phys.

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In this work, we study the realization of non-invertible duality symmetries along the toroidal branch of the c = 2 conformal manifold. A systematic procedure to construct symmetry defects is implemented to show that all Rational Conformal Field Theories along this branch enjoy duality symmetries. Furthermore, we delve into an in-depth analysis of two representative cases of multicritical theories, where the toroidal branch meets various orbifold branches. For these particular examples, the categorical data and the defect Hilbert spaces associated with the duality symmetries are obtained by resorting to modular covariance. Finally, we study the interplay between these novel symmetries and the various exactly marginal and relevant deformations, including some representative examples of Renormalization Group flows where the infrared is constrained by the non-invertible symmetries and their anomalies.

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Unifying constructions of non-invertible symmetries

Cited by 29 publications

References 58 publications

Generalized charges, part I: Invertible symmetries and higher representations

Generalized charges, part I: Invertible symmetries and higher representations

Generalized symmetries and anomalies of 3d $\mathcal{N}=4$ SCFTs

Exploring duality symmetries, multicriticality and RG flows at c = 2

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