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

Abstract

We systematically study 4D $\mathcal{N}=2$ superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ${\mathbb{C}}^4$. We show that if a theory in this class has no $\mathcal{N}=2$-preserving exactly marginal deformation (i.e., the theory is isolated as an $\mathcal{N}=2$ 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 $a<\frac{1}{24}(15r+2f)$ and $c<\frac{1}{6}(3r+f)$ (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 $\mathcal{N}=2$ SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

84 pages; v2: references added, minor typos fixed, minor additional result (direct proof of corollary 1)

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Cited by in corpus (21)

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• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• 2-Group Symmetries and M-Theory
• Higher Symmetries of 5d Orbifold SCFTs
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Anomalies of Generalized Symmetries from Solitonic Defects
• Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• Disconnected 0-Form and 2-Group Symmetries
• Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• On the Protected Spectrum of the Minimal Argyres-Douglas Theory
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers