Coulomb and Higgs branches from canonical singularities. Part 0

Closset, Cyril; Schäfer‐Nameki, Sakura; Wang, Yinan

doi:10.1007/jhep02(2021)003

Cited by 155 publications

(339 citation statements)

References 143 publications

(333 reference statements)

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“…Much progress has been made on mapping out the theories in 6d, including a putative classification of SCFTs [2][3][4][5] and LSTs [5,6] from F-theory on elliptic Calabi-Yau three-folds -for a review of the 6d classification, see [7]. In 5d recent progress has been made in mapping out and furthering the classification of SCFTs using the M-theory realization on canonical singularities [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Jhep02(2021)159mentioning

confidence: 99%

“…From a geometric engineering point of view, higher form symmetries were discussed using the M-theory realization of 5d SCFTs on Calabi-Yau threefolds, as well as other M-theory geometric engineering constructions such as G 2 -holonomy compactifications to 4d in [23,27,28]. Related works in Type IIB, for 4d SCFTs in particular Argyres-Douglas theories were obtained in [25,29,30]. In 6d the defect group was analyzed in [31] and the 1-form symmetries in 6d SCFTs were discussed from a geometric construction in [27].…”

Section: Jhep02(2021)159mentioning

confidence: 99%

“…It is this above mentioned choice of discrete data that gives rise to the 5d theories in the above mentioned class of 5d theories that we will be studying 10. Just like the case of 1-form and 2-form symmetries of 6d theories, these 1-form symmetries of 5d theories will also be spontaneously broken in all kinds of vacua we discuss below.11 See however[25] for some proposed counter-examples. In these cases, there are 3-form symmetries, whose interpretation remains to be fully understood in terms of the classification of 5d SCFTs.…”

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confidence: 97%

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Higher-form symmetries of 6d and 5d theories

Bhardwaj

Schäfer‐Nameki

2021

J. High Energ. Phys.

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114

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We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

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Section: Jhep02(2021)159mentioning

confidence: 99%

Section: Jhep02(2021)159mentioning

confidence: 99%

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confidence: 97%

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Higher-form symmetries of 6d and 5d theories

Bhardwaj

Schäfer‐Nameki

2021

J. High Energ. Phys.

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114

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“…So far the MQs were derived indirectly either from the knowledge of the moduli space, or using brane-webs. The MQ can be determined also for 5d SCFTs realized as M-theory on canonical three-fold singularities by employing string dualities, and relating this to 4d SCFT in Type IIB obtained from the same canonical singularity [33]. Further compactifying to 3d and using mirror symmetry, i.e.…”

Section: Magnetic Quivers Flavor Symmetry and Hasse Diagramsmentioning

confidence: 99%

“…Compared to the status of the extended CB, it is less clear how one can in general determine the structure of the HB from the geometry. A precise correspondence of the deformation space of the Calabi-Yau singularity and the HB of the associated 5d SCFT has only been achieved for singularities that can be realized as strictly convex toric polygons [31,32] and, recently, for isolated hyper-surface singularities [33].…”

Section: Introductionmentioning

confidence: 99%

(5d RG-flow) trees in the tropical rain forest

Beest

Bourget

Eckhard

et al. 2021

J. High Energ. Phys.

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5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in [1], which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries.

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The Branes Behind Generalized Symmetry Operators

Heckman

Hübner

Torres

et al. 2022

Fortschritte der Physik

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The modern approach to m-form global symmetries in a d-dimensional quantum field theory (QFT) entails specifying dimension d − m − 1 topological generalized symmetry operators which non-trivially link with m-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry X, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary 𝝏X. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in 𝝏X. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

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Coulomb and Higgs branches from canonical singularities. Part 0

Cited by 155 publications

References 143 publications

Higher-form symmetries of 6d and 5d theories

Higher-form symmetries of 6d and 5d theories

(5d RG-flow) trees in the tropical rain forest

The Branes Behind Generalized Symmetry Operators

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