Tinkertoys for Gaiotto Duality

Abstract

We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N=5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N=2 SCFTs.

61 pages, 136 figures (a veritable comic book). V2: Grotty bitmapped figures replaced with PDF versions; a couple of references fixed

References in corpus (10)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• S-duality in N=2 supersymmetric gauge theories
• Webs of five-branes and N=2 superconformal field theories
• Mirrors of 3d Sicilian theories
• Sicilian gauge theories and N=1 dualities
• A holographic computation of the central charges of d=4, N=2 SCFTs
• The Superconformal Index of the E_6 SCFT
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories
• Argyres-Seiberg duality and the Higgs branch

Cited by in corpus (127)

• Infinite Chiral Symmetry in Four Dimensions
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Gauge Theories and Macdonald Polynomials
• Four-Dimensional SCFTs from M5-Branes
• 4d Index to 3d Index and 2d TQFT
• N=1 Deformations and RG Flows of N=2 SCFTs
• Wild Quiver Gauge Theories
• Tinkertoys for the D_N series
• Chiral algebras of class S
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Tinkertoys for the Twisted D-Series
• Exceptional Indices
• Topological strings and 5d T_N partition functions
• Stress-tensor OPE in N=2 Superconformal Theories
• N=2 supersymmetric dynamics for pedestrians
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• Trifectas for $T_N$ in 5d
• New N=1 Dualities
• 2-Group Symmetries in Class S
• Lifting 4d dualities to 5d
• Central charges and RG flow of strongly-coupled N=2 theory
• Chiral Algebras for Trinion Theories
• Quiver Tails and N=1 SCFTs from M5-branes
• Classification of 4d N=2 gauge theories
• Exact results for 5d SCFTs of long quiver type
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Tackling the SDC in AdS with CFTs
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• M5 brane and four dimensional N=1 theories I
• The Superconformal Index of Class S Theories of Type D
• New aspects of Argyres--Douglas theories and their dimensional reduction
• Tri-vertices and SU(2)'s
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• Brane webs, $5d$ gauge theories and $6d$ $\mathcal{N}$$=(1,0)$ SCFT's
• Mass-deformed $T_N$ as a linear quiver
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Comments on scaling limits of 4d N=2 theories
• A review of the T_N theory and its cousins
• Argyres-Douglas Theories and S-Duality
• M5-brane Sources, Holography, and Argyres-Douglas Theories
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• 2d TQFT structure of the superconformal indices with outer-automorphism twists
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• More Three Dimensional Mirror Pairs
• Central Charges of 2d Superconformal Defects
• Seiberg-Witten Geometries Revisited
• Global Form of Flavor Symmetry Groups in 4d N=2 Theories of Class S
• Higher Derivative Corrections and Central Charges from Wrapped M5-branes
• Anomaly Inflow for M5-branes on Punctured Riemann Surfaces
• N=1 conformal dualities
• A "Lagrangian" for the E7 Superconformal Theory
• Magnetic Lattices for Orthosymplectic Quivers
• A slow review of the AGT correspondence
• New N=2 superconformal field theories from S-folds
• Towards a 4d/2d correspondence for Sicilian quivers
• New N=1 Dualities from M5-branes and Outer-automorphism Twists
• Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface
• N=2 Generalized Superconformal Quiver Gauge Theory
• Tinkertoys for the E7 Theory
• N=1 Geometries via M-theory
• Folding Orthosymplectic Quivers
• On 6d N=(2,0) theory compactified on a Riemann surface with finite area
• Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories
• BPS Graphs: From Spectral Networks to BPS Quivers
• Coulomb branches with complex singularities
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• 5d fixed points from brane webs and O7-planes
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• An N=1 Lagrangian for the rank 1 E6 superconformal theory
• An N=1 Lagrangian for an N=3 SCFT
• Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories
• Argyres-Douglas Theories in Class S Without Irregularity
• BPS spectrum of Argyres-Douglas theory via spectral network
• T-branes, monopoles and S-duality
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
• Four dimensional superconformal theories from M5 branes
• The moduli space of vacua of N=2 class S theories
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• Compactifications of 5d SCFTs with a twist
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Higgs branch RG-flows via Decay and Fission
• Higgs, Coulomb, and Hall-Littlewood
• Probing 7-branes on Orbifolds
• $\mathcal{N}=1$ superconformal theories with $D_N$ blocks
• Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow
• Green-Schwarz Automorphisms and 6D SCFTs
• Mirror Symmetry in Three Dimensions via Gauged Linear Quivers
• A geometric recipe for twisted superpotentials
• Argyres-Douglas matter and S-duality: Part II
• Singular points in N=2 SQCD
• The Higgs branch of Heterotic ALE instantons
• Wrapped Branes and Punctured Horizons
• Brane webs in the presence of an $O{5}^{-}$-plane and 4d class S theories of type D
• Comments on the twisted punctures of $A_{\text{even}}$ class S theory
• Exploring the orthosymplectic zoo
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• On minimal Type IIB $Ad{S}_6$ solutions with commuting 7-branes
• Seiberg-Witten for $Spin(n)$ with Spinors
• Coulomb Branches of Star-Shaped Quivers
• The ABCDEFG of Little Strings
• Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d N=2 supersymmetric theories
• Little String Origin of Surface Defects
• An infrared bootstrap of the Schur index with surface defects
• Masses, Sheets and Rigid SCFTs
• Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings
• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• Isomorphisms of 4d N=2 SCFTs from 6d
• On low rank 4d $\mathcal{N}=2$ SCFTs
• 1-form Symmetries of 4d N=2 Class S Theories
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• Quiver Polymerisation
• The Grassmannian VOA
• Singular SQCD Vacua and Confinement
• Weak Coupling Limits and Colliding Punctures in Class-S Theories
• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
• New Dualities and Misleading Anomaly Matchings from Outer-automorphism Twists
• Families of Hitchin systems and N=2 theories
• The Hitchin Image in Type-D
• Aspects of 4d supersymmetric dynamics and geometry
• A Note on the Stringy Embeddings of Certain N = 2 Dualities