Coulomb and Higgs Branches from Canonical Singularities: Part 0

Abstract

Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $\mathcal{N}=4$ mirror symmetry and an $S$-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type $(G,G^{\prime })$.

64 pages; v2: fixed typos, added references and clarifications. v3: more references added; v4: fixed refs and typos, JHEP version; v5: small corrections and updated references

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• Heisenberg Groups and Noncommutative Fluxes
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• Down the rabbit hole with theories of class S
• Lagrangians for generalized Argyres-Douglas theories
• Coulomb Branch and The Moduli Space of Instantons
• Higher Form Symmetries and M-theory
• Trifectas for $T_N$ in 5d
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• N=1 Lagrangians for generalized Argyres-Douglas theories
• Magnetic quivers for rank 1 theories
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• Higher Form Symmetries of Argyres-Douglas Theories
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Cited by in corpus (85)

• The Branes Behind Generalized Symmetry Operators
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Higher-form symmetries of 6d and 5d theories
• Lecture Notes on Generalized Symmetries and Applications
• 2-Group Symmetries in Class S
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• Symmetry TFTs for 3d QFTs from M-theory
• 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
• (5d RG-flow) Trees in the Tropical Rain Forest
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Instantons, Symmetries and Anomalies in Five Dimensions
• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
• Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Flavor Symmetry of 5d SCFTs, Part 2: Applications
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Anomalies of Generalized Symmetries from Solitonic Defects
• Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions
• Magnetic quivers for rank 2 theories
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Zero-form and one-form symmetries of the ABJ and related theories
• Fibrations and Hasse diagrams for 6d SCFTs
• $\mathcal{N}=2^{\ast }$ Schur indices
• Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories
• Higgs Branches of U/SU Quivers via Brane Locking
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Higgs, Coulomb, and Hall-Littlewood
• Higgs branch RG-flows via Decay and Fission
• Decay and Fission of Magnetic Quivers
• Supersymmetry breaking deformations and phase transitions in five dimensions
• Discrete gauging and Hasse diagrams
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• The Cat's Cradle: Deforming the higher rank $E_1$ and ${\tilde{E}}_1$ theories
• Genus zero Gopakumar-Vafa invariants from open strings
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities
• Exploring the orthosymplectic zoo
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Flops of any length, Gopakumar-Vafa invariants, and 5d Higgs Branches
• Fibre-base duality of 5d KK theories
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• The Fate of Discrete 1-Form Symmetries in 6d
• Orthosymplectic Quotient Quiver Subtraction
• Noncommutative Instantons in Diverse Dimensions
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• On the Protected Spectrum of the Minimal Argyres-Douglas Theory
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• On low rank 4d $\mathcal{N}=2$ SCFTs
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches
• 1-form Symmetries of 4d N=2 Class S Theories
• Quiver Polymerisation
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory
• From Regular to Irregular: A Unified Origin for Argyres-Douglas Theories
• Magnetic quivers from brane webs with O7${}^{+}$-planes
• FI-flows of 3d N=4 Theories
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• Symmetry TFTs from String Theory