Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions

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

doi:10.48550/arxiv.2111.13564

Cited by 8 publications

(27 citation statements)

References 68 publications

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“…IHSs can be classified and we refer to this as the Kreuzer-Skarke-Yau-Yu (KS-YY) classification [79,85]. To specify an IHS we will use the notation in [55], which indicates the type and vanishing orders of P .…”

Section: The Defect Group Of Type Iib On Ihsmentioning

confidence: 99%

“…Striking examples of trapped 1-form symmetries are provided by Argyres-Douglas (AD) theories of type AD[G, G ] that are constructed by compactifying 6d N = (2, 0) theories on a sphere with a single puncture that is irregular. Such AD theories, and also a vast number of other 4d N = 2 SCFTs, can also be constructed by compactifying Type IIB on canonical isolated hypersurface Calabi-Yau three-fold singularities (IHS) X [17,29,30,36,55,[75][76][77][78][79][80][81][82][83][84][85][86], for a recent review see [87]. Using string theoretic methods, the 1-form symmetries of these 4d N = 2 SCFTs can be computed from the topology of the boundary 5-manifold ∂X [17,29,30,36,55].…”

Section: Introductionmentioning

confidence: 99%

“…Such AD theories, and also a vast number of other 4d N = 2 SCFTs, can also be constructed by compactifying Type IIB on canonical isolated hypersurface Calabi-Yau three-fold singularities (IHS) X [17,29,30,36,55,[75][76][77][78][79][80][81][82][83][84][85][86], for a recent review see [87]. Using string theoretic methods, the 1-form symmetries of these 4d N = 2 SCFTs can be computed from the topology of the boundary 5-manifold ∂X [17,29,30,36,55].…”

Section: Introductionmentioning

confidence: 99%

“…The monodromy of the Higgs field around the puncture captures the monodromy of the ALE fibration. Now one can apply the tools developed in [17,29,30,36,55] to deduce this piece of the defect group of the puncture from the data of the monodromy of the ALE fibration. However, this doesn't provide full information related to the defect group.…”

Section: Introductionmentioning

confidence: 99%

“…Second, for the IHS punctures, the trapped part of the defect group can be computed using Type IIB compactified on the corresponding IHS singularity, using the technology developed in [17,29,30,36,55]. The obtained trapped defect group can then be checked against the trapped defect group predicted by the conjecture.…”

Section: Introductionmentioning

confidence: 99%

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Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S

Bhardwaj¹,

Giacomelli²,

Hübner³

et al. 2022

Preprint

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A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are 6d N = (2, 0) theories that are boundary conditions of 7d TQFTs, with the defect group arising from surface defects. In this paper, we study codimension-two defects in 6d N = (2, 0) theories, and find that the line defects living inside these codimension-two defects are mutually non-local and hence also form a defect group. Thus, codimension-two defects in a 6d N = (2, 0) theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the 7d bulk TQFT. A codimension-two defect carrying a non-trivial defect group acts as an irregular puncture when used in the construction of 4d N = 2 Class S theories. The defect group associated to such an irregular puncture provides extra "trapped" contributions to the 1-form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and non-conformal irregular punctures. Along the way, we discover many new classes of irregular punctures. A key role in the analysis of defect groups is played by two different geometric descriptions of the punctures in Type IIB string theory: one provided by isolated hypersurface singularities in Calabi-Yau threefolds, and the other provided by ALE fibrations with monodromies.

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Section: The Defect Group Of Type Iib On Ihsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S

Bhardwaj¹,

Giacomelli²,

Hübner³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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Zero-form and one-form symmetries of the ABJ and related theories

Beratto

Mekareeya

Sacchi

2022

J. High Energ. Phys.

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The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis (ABJ) and related theories, with at least $$ \mathcal{N} $$ N = 6 supersymmetry in three dimensions, are examined in detail. Starting from well-known dualities between theories with orthogonal and symplectic gauge groups and those with unitary gauge groups, we gauge their one-form symmetries or their subgroups and obtain new dualities. One side of the latter involves theories with special orthogonal and symplectic gauge groups, and the other side involves theories with unitary gauge groups; there is a discrete quotient on one or both sides of the duality. We study the refined superconformal indices of such theories and map the symmetries across the dualities, with particular attention to their discrete part. As a generalisation, we also find a new duality between a circular quiver with a discrete quotient of alternating special orthogonal and symplectic gauge groups and a three-dimensional $$ \mathcal{N} $$ N = 4 circular (Kronheimer-Nakajima) quiver with unitary gauge groups, whose Higgs or Coulomb branch describes an instanton on a singular orbifold.

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5D and 6D SCFTs from $\mathbb{C}^3$ orbifolds

Tian

Wang

2022

SciPost Phys.

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We study the orbifold singularities X=\mathbb{C}^3/\GammaX=ℂ3/Γ where \GammaΓ is a finite subgroup of SU(3)SU(3). M-theory on this orbifold singularity gives rise to a 5d SCFT, which is investigated with two methods. The first approach is via 3d McKay correspondence which relates the group theoretic data of \GammaΓ to the physical properties of the 5d SCFT. In particular, the 1-form symmetry of the 5d SCFT is read off from the McKay quiver of \GammaΓ in an elegant way. The second method is to explicitly resolve the singularity XX and study the Coulomb branch information of the 5d SCFT, which is applied to toric, non-toric hypersurface and complete intersection cases. Many new theories are constructed, either with or without an IR quiver gauge theory description. We find that many resolved Calabi-Yau threefolds, \widetilde{X}X̃, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of \GammaΓ, the orbifold singularity \mathbb{C}^3/\Gammaℂ3/Γ can be embedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the F-theory construction. Such 6d theory is naturally related to the 5d SCFT defined on the same singularity. We find examples of rank-1 6d SCFTs without a gauge group, which are potentially different from the rank-1 E-string theory.

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Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions

Cited by 8 publications

References 68 publications

Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S

Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S

Zero-form and one-form symmetries of the ABJ and related theories

5D and 6D SCFTs from $\mathbb{C}^3$ orbifolds

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