Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories

Hosseini, Saghar S.; Moscrop, Robert

doi:10.48550/arxiv.2106.03878

Cited by 6 publications

(11 citation statements)

References 33 publications

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“…In the next section we will review this result and use it to compute the defect group of orbifold singularities. Moreover, we will confirm the same result exploiting the corresponding 5d BPS quivers, building on [32,82].…”

Section: Defect Groups and Higher Symmetries In 5dsupporting

confidence: 72%

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: Defect Groups and Higher Symmetries In 5dsupporting

confidence: 72%

Higher Symmetries of 5d Orbifold SCFTs

Del Zotto,

Heckman,

Meynet

et al. 2022

Preprint

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“…Claim 3: IHS theories with i q i > 3/2 are isolated 4D N = 2 SCFTs. 25 Proof: We give two proofs of this statement. The first follows from unitarity bounds in the (possibly trivial!)…”

Section: Some Rigorous Bounds and A (Less Rigorous) Conjecturementioning

confidence: 98%

“…where we can have b = h ∨ , and G b (k) is in our class of SCFTs. We may use similar logic to that used for b = h ∨ to conclude that, if we can equate the UV and IR 1-form symmetries (as assumed in [25] and as hinted at by the agreement of the UV and IR ranks), the D b k (G) theories have 1-form symmetry only if they are part of a conformal manifold. Furthermore, if one can identify 1-form symmetry in certain more general flows between theories related to IHSs embedded in C * × C 3 and those related to IHSs embedded in C 4 , then we expect the above comments to generalize.…”

Section: Comments On 1-form Symmetries In More General Isolated N ≥ 2...mentioning

confidence: 99%

1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds

Buican,

Jiang

2021

Preprint

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We systematically study 4D N = 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in C 4 . We show that if a theory in this class has no N = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an N = 2 SCFT), then it has no 1-form symmetry.This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying a < 1 24 (15r + 2f ) and c < 1 6 (3r + f ) (where r is the complex dimension of the Coulomb branch, and f is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D N = 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

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“…The main difference is that the theories without a principal polarization will have a non-trivial global structure, see e.g. [20,21,[41][42][43][44][45][46] for some recent studies on the topic of 1-form symmetries of N = 2 SCFTs. Moreover, this assumption is really strictly necessary only for (2.21), the following equations are true independently from it.…”

Section: Arithmetics Of the Characteristic Symmetrymentioning

confidence: 99%

The Characteristic Dimension of Four-dimensional $\mathcal{N} = 2$ SCFTs

Cecotti¹,

Zotto²,

Martone³

et al. 2021

Preprint

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In this paper we introduce the characteristic dimension of a four dimensional N = 2 superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We prove that only nine values of the characteristic dimension are allowed, −∞, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving a new organizing principle to the vast landscape of 4d N = 2 SCFTs. Whenever the characteristic dimension differs from 1 or 2, only very constrained special Kähler geometries (i.e. isotrivial, diagonal and rigid) are compatible with the corresponding set of Coulomb branch dimensions and extremely special, maximally strongly coupled, BPS spectra are allowed for the theories which realize them. Our discussion applies to superconformal field theories of arbitrary rank, i.e. with Coulomb branches of any complex dimension. Along the way, we predict the existence of new N = 3 theories of rank two with non-trivial one-form symmetries.

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Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories

Cited by 6 publications

References 33 publications

Higher Symmetries of 5d Orbifold SCFTs

Higher Symmetries of 5d Orbifold SCFTs

1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds

The Characteristic Dimension of Four-dimensional $\mathcal{N} = 2$ SCFTs

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