Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2

Abstract

We study compactification of 6 dimensional (1,0) theories on T^2. We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d N=2 geometry for a large number of the (1,0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4d N=2 SCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL(2,Z) duality symmetry inherited from global diffeomorphisms of the T^2. This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T^2. Among the resulting 4d N=2 CFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of class S with punctures from toroidal compactification of (1,0) SCFTs where the curve of the class S theory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class S theories with no punctures on arbitrary genus Riemann surface.

58 pages, 8 figures, v2: references added, typos fixed, table 2 updated

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• Holography for (1,0) theories in six dimensions
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• Six-Dimensional Superconformal Theories and their Compactifications from Type IIA Supergravity
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Categorical Tinkertoys for N=2 Gauge Theories
• Argyres-Douglas Theories and S-Duality
• Charting Class ${\mathcal{S}}_k$ Territory
• Little strings and T-duality
• Classification of 6d N=(1,0) gauge theories
• N=1 theories of class S_k
• 6d $\mathcal{N}=(1,0)$ theories on $T^2$ and class S theories: part I
• Supersymmetric Partition Functions and a String Theory in 4 Dimensions
• RG flows from (1,0) 6D SCFTs to N=1 SCFTs in four and three dimensions

Cited by in corpus (90)

• On the Superconformal Index of Argyres-Douglas Theories
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• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• 6D SCFTs and Phases of 5D Theories
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Classification of Argyres-Douglas theories from M5 branes
• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• IIB flux non-commutativity and the global structure of field theories
• E-String Theory on Riemann Surfaces
• 6d SCFTs, 5d Dualities and Tao Web Diagrams
• D-type Conformal Matter and SU/USp Quivers
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Compactification of 6d minimal SCFTs on Riemann surfaces
• Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Higher Form Symmetries of Argyres-Douglas Theories
• Rank $Q$ E-string on a torus with flux
• Compactifications of ADE conformal matter on a torus
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Conformal Manifolds in Four Dimensions and Chiral Algebras
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries
• Brane webs, $5d$ gauge theories and $6d$ $\mathcal{N}$$=(1,0)$ SCFT's
• On Irregular Singularity Wave Functions and Superconformal Indices
• On Exceptional Instanton Strings
• Aspects of Superconformal Multiplets in D>4
• AdS${}_7$/CFT${}_6$ with orientifolds
• Revisiting the classifications of 6d SCFTs and LSTs
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• 4D Gauge Theories with Conformal Matter
• F-Theory and N=1 SCFTs in Four Dimensions
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Towards Classification of 5d SCFTs: Single Gauge Node
• Small instanton transitions for M5 fractions
• Fine Tuning, Sequestering, and the Swampland
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Chiral theories of class S
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• AdS5 compactifications with punctures in massive IIA supergravity
• Dual Little Strings from F-Theory and Flop Transitions
• Tinkertoys for the E7 Theory
• From 6D SCFTs to Dynamic GLSMs
• $\mathcal{N}=2^{\ast }$ Schur indices
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• 6d $\mathcal{N}=(1,0)$ theories on $S^1/T^2$ and class S theories: part II
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• 4d N=2 SCFT and singularity theory Part I: Classification
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• On the chiral algebra of Argyres-Douglas theories and S-duality
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• Non-Simply-Connected Symmetries in 6D SCFTs
• 6d strings and exceptional instantons
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• M5-branes Probing Flux Backgrounds
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Higgs, Coulomb, and Hall-Littlewood
• Compactifications of 5d SCFTs with a twist
• On the torus compactifications of $Z_2$ orbifolds of E-string theories
• Argyres-Douglas matter and N=2 dualities
• D-type fiber-base duality
• Green-Schwarz Automorphisms and 6D SCFTs
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Argyres-Douglas matter and S-duality: Part II
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• ADE String Chains and Mirror Symmetry
• 4d N=1 from 6d N=(1,0) on a torus with fluxes
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking
• Expanding the landscape of $\mathcal{N}$=2 rank 1 SCFTs
• Infinitely many 4d N=1 SCFTs with a=c
• Nilpotent Networks and 4D RG Flows
• The ABCDEFG of Little Strings
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• On the Nekrasov Partition Function of Gauged Argyres-Douglas Theories
• Little String Defects and Bala-Carter Theory
• Landau-Ginzburg skeletons
• Homological S-Duality in 4d N=2 QFTs
• Seiberg-Witten differential via primitive forms
• K3 metrics from little string theory
• Higher S-dualities and Shephard-Todd groups
• Punctures and Dynamical Systems
• S-duality invariant perturbation theory improved by holography
• Isomorphisms of 4d N=2 SCFTs from 6d
• M-strings in thermodynamic limit: Seiberg-Witten geometry
• The Geometry of Decoupling Fields
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Mixed Hodge structure and $\mathcal{N}=2$ Coulomb branch solution
• New Dualities and Misleading Anomaly Matchings from Outer-automorphism Twists