3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry

Nawata, Satoshi; Sperling, Marcus; Wang, Hao Ellery; Zhong, Zhenghao

doi:10.21468/scipostphys.15.1.033

Cited by 7 publications

(3 citation statements)

References 74 publications

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“…A paper with related results will appear at the same time in [101]. We thank the authors for coordinating submission.…”

Section: Generalization To T[su(n)]mentioning

confidence: 87%

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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“…A paper with related results will appear at the same time in [101]. We thank the authors for coordinating submission.…”

Section: Generalization To T[su(n)]mentioning

confidence: 87%

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

Bhardwaj,

Bullimore,

Ferrari

et al. 2024

SciPost Phys.

View full text Add to dashboard Cite

show abstract

“…The edge multiplicity and double lace on Coulomb branch cannot be distinguished; the difference is manifest on the Higgs branch, which is left to future work. Moreover, the two potential theory also differ in their higher symmetries, as recently analysed in [17,25,35].…”

Section: Kleinian a With Z Q Quotientmentioning

confidence: 94%

“…A second result of this work is to realise orbifold actions on the Coulomb branch by turning simply laced edges into non-simply laced edges [15]. The relationships between quivers with simply laced and non-simply laced edges were studied in [16,17] and are studied further here.…”

Section: Jhep05(2024)318 1 Introductionmentioning

confidence: 99%

Actions on the quiver: discrete quotients on the Coulomb branch

Hanany,

Kumaran,

et al. 2024

J. High Energ. Phys.

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This paper introduces two operations in quiver gauge theories. The first operation, collapse, takes a quiver with a permutation symmetry Sn and gives a quiver with adjoint loops. The corresponding 3d $$ \mathcal{N} $$ N = 4 Coulomb branches are related by an orbifold of Sn. The second operation, multi-lacing, takes a quiver with n nodes connected by edges of multiplicity k and replaces them by n nodes of multiplicity qk. The corresponding Coulomb branch moduli spaces are related by an orbifold of type $$ {\mathbb{Z}}_q^{n-1} $$ ℤ q n − 1 . Collapse generalises known cases that appeared in the literature [1–3]. These two operations can be combined to generate new relations between moduli spaces that are constructed using the magnetic construction.

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A tale of N cones

Bourget,

Grimminger,

Hanany

et al. 2023

J. High Energ. Phys.

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We study particular families of bad 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories, whose Higgs branches consist of many cones. We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone. Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches. These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring). Applying the principle of inversion to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams. These Coulomb branches have several most singular loci, corresponding to the several cones in the Higgs branch. We propose the Hasse diagrams of the full quantum moduli spaces of our theories. The quivers we study can be taken to be 5d effective gauge theories living on brane webs. Their infinite coupling theories have Higgs branches which also consist of multiple cones. Some of these cones have decorated magnetic quivers, whose 3d Coulomb branches remain elusive.

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3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry

Cited by 7 publications

References 74 publications

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

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

Actions on the quiver: discrete quotients on the Coulomb branch

A tale of N cones

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