Comments on Global Symmetries and Anomalies of $5d$ SCFTs

Genolini, Pietro Benetti; Tizzano, Luigi

doi:10.48550/arxiv.2201.02190

Cited by 12 publications

(13 citation statements)

References 61 publications

(166 reference statements)

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“…Recently the physics and geometry of many such singularities were studied in references [50,51]. For further discussion of higher-form symmetries in 5d SCFTs, see in particular [17,18,33,52,53]. For additional background on geometric engineering and 5d SCFTs, see [54][55][56][57][58][59][60][61][62][63][64][65] as well as [66][67][68][69][70][71][72][73][74].…”

Section: Introductionmentioning

confidence: 99%

Higher Symmetries of 5d Orbifold SCFTs

Del Zotto,

Heckman,

Meynet

et al. 2022

Preprint

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We determine the higher symmetries of 5d SCFTs engineered from M-theory on a C 3 /Γ background for Γ a finite subgroup of SU (3). This resolves a longstanding question as to how to extract this data when the resulting singularity is non-toric (when Γ is non-abelian) and/or not isolated (when the action of Γ has fixed loci). The BPS states of the theory are encoded in a 1D quiver quantum mechanics gauge theory which determines the possible 1-form and 2-form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0-form symmetry, the abelianization of Γ detects a 2-group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.

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Section: Introductionmentioning

confidence: 99%

Higher Symmetries of 5d Orbifold SCFTs

Del Zotto,

Heckman,

Meynet

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently the physics and geometry of many such singularities were studied in references [50,51]. For further discussion of higher-form symmetries in 5D SCFTs, see in particular [17,18,33,52,53]. For additional background on geometric engineering and 5D SCFTs, see [54][55][56][57][58][59][60][61][62][63][64][65] as well as [66][67][68][69][70][71][72][73][74].…”

Section: Introductionmentioning

confidence: 99%

Higher symmetries of 5D orbifold SCFTs

et al. 2022

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We determine the higher symmetries of 5D SCFTs engineered from M-theory on a C 3 =Γ background for Γ a finite subgroup of SUð3Þ. This resolves a longstanding question as to how to extract this data when the resulting singularity is nontoric (when Γ is non-Abelian) and/or not isolated (when the action of Γ has fixed loci). The Bogomol'nyi-Prasad-Sommerfield (BPS) states of the theory are encoded in a 1D quiver quantum mechanics gauge theory which determines the possible 1-form and 2-form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0-form symmetry, the abelianization of Γ detects a 2-group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.

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“…4 For recent work on the physics of 2-groups, see e.g. [10,[21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds

Cvetič¹,

Heckman²,

Hübner³

et al. 2022

Preprint

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Orbifold singularities of M-theory constitute the building blocks of a broad class of supersymmetric quantum field theories (SQFTs). In this paper we show how the local data of these geometries determines global data on the resulting higher symmetries of these systems. In particular, via a process of cutting and gluing, we show how local orbifold singularities encode the 0-form, 1-form and 2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from the possible singularities which extend to the boundary of the non-compact geometry. The resulting category of boundary conditions then captures these symmetries, and is equivalently specified by the orbifold homology of the boundary geometry. We illustrate these general points in the context of a number of examples, including 5D superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as 4D SQCD-like theories engineered via M-theory on non-compact G 2 spaces.

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Comments on Global Symmetries and Anomalies of $5d$ SCFTs

Cited by 12 publications

References 61 publications

Higher Symmetries of 5d Orbifold SCFTs

Higher Symmetries of 5d Orbifold SCFTs

Higher symmetries of 5D orbifold SCFTs

0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds

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