Superconformal Fixed Points with E_n Global Symmetry

Abstract

We obtain the elliptic curve and the Seiberg-Witten differential for an $N=2$ superconformal field theory which has an $E_8$ global symmetry at the strong coupling point $\tau =e^{\pi i/3}$. The differential has 120 poles corresponding to half the charged states in the fundamental representation of $E_8$, with the other half living on the other sheet. Using this theory, we flow down to $E_7$, $E_6$ and $D_4$. A new feature is a ${\lambda }_{SW}$ for these theories based on their adjoint representations. We argue that these theories have different physics than those with ${\lambda }_{SW}$ built from the fundamental representations.

23 pages, harvmac (b), Mathematica file available at http://physics.usc.edu/~minahan/Math/e8.ma

References in corpus (6)

• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• F-Theory at Constant Coupling
• BPS States of Exceptional Non-Critical Strings
• Toroidal Compactification of Heterotic 6D Non-Critical Strings Down to Four Dimensions

Cited by in corpus (174)

• Infinite Chiral Symmetry in Four Dimensions
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Gauge Theories and Macdonald Polynomials
• Beyond eta/s = 1/4pi
• S-duality in N=2 supersymmetric gauge theories
• Webs of five-branes and N=2 superconformal field theories
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• Mirrors of 3d Sicilian theories
• Tinkertoys for Gaiotto Duality
• T-Branes and Monodromy
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• Sicilian gauge theories and N=1 dualities
• N=1 Deformations and RG Flows of N=2 SCFTs
• Five-branes, Seven-branes and Five-dimensional E_n field theories
• The $\mathcal{N}=2$ superconformal bootstrap
• On the Superconformal Index of Argyres-Douglas Theories
• The Hilbert Series of the One Instanton Moduli Space
• Wild Quiver Gauge Theories
• Tinkertoys for the D_N series
• Large N Superconformal Gauge Theories and Supergravity Orientifolds
• The Omega deformed B-model for rigid N=2 theories
• 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
• Non-Lagrangian Theories from Brane Junctions
• Top Down Approach to 6D SCFTs
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• More on the N=2 superconformal systems of type $D_p(G)$
• Tinkertoys for the Twisted D-Series
• Exceptional Indices
• Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories
• Infinitely many N=2 SCFT with ADE flavor symmetry
• 750 GeV Diphotons from a D3-brane
• On Painlevé/gauge theory correspondence
• N=2 supersymmetric dynamics for pedestrians
• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• E-String Theory on Riemann Surfaces
• Central charges and RG flow of strongly-coupled N=2 theory
• The Point of E_8 in F-theory GUTs
• Chiral Algebras for Trinion Theories
• Argyres-Seiberg duality and the Higgs branch
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• On 4d rank-one N=3 superconformal field theories
• Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Field Theory Questions for String Theory Answers
• Constraints on the BPS Spectrum of N = 2, D = 4 Theories with A-D-E Flavor Symmetry
• Hilbert Series for Moduli Spaces of Two Instantons
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• 8d Supergravity, Reconstruction of Internal Geometry and the Swampland
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• Baryon and Dark Matter Genesis from Strongly Coupled Strings
• Rank $Q$ E-string on a torus with flux
• Constraints on Chiral Operators in N=2 SCFTs
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• The Superconformal Index of Class S Theories of Type D
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Brane webs, $5d$ gauge theories and $6d$ $\mathcal{N}$$=(1,0)$ SCFT's
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Counting Exceptional Instantons
• A review of the T_N theory and its cousins
• 4d $\mathcal{N}=2$ S-folds
• On Exceptional Instanton Strings
• N = 1 SCFTs from Brane Monodromy
• An Exceptional Sector for F-theory GUTs
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• Non-Critical Strings, Del Pezzo Singularities And Seiberg-Witten Curves
• 4D Gauge Theories with Conformal Matter
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• RG flows with supersymmetry enhancement and geometric engineering
• Seiberg-Witten Curve for the E-String Theory
• More Three Dimensional Mirror Pairs
• Matter From G(2) Manifolds
• Gaiotto Duality for the Twisted A_{2N-1} Series
• Extra $W$-Boson Mass from a D3-Brane
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Anomaly matching on the Higgs branch
• N=2 S-duality via Outer-automorphism Twists
• A slow review of the AGT correspondence
• A "Lagrangian" for the E7 Superconformal Theory
• 5d $E_n$ Seiberg-Witten curve via toric-like diagram
• New N=2 superconformal field theories from S-folds
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• New N=1 Dualities from M5-branes and Outer-automorphism Twists
• Electroweak Symmetry Breaking in the DSSM
• Mordell-Weil Lattice via String Junctions
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Tinkertoys for the E7 Theory
• From 6D SCFTs to Dynamic GLSMs
• Affine Lie Algebras, String Junctions and 7-Branes
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• N=2 Superconformal Field Theory with ADE Global Symmetry on a D3-brane Probe
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• VOAs and rank-two instanton SCFTs
• Non-Abelian Conifold Transitions and N=4 Dualities in Three Dimensions
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• N=2 SU Quiver with USP Ends or SU Ends with Antisymmetric Matter
• Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• 5d fixed points from brane webs and O7-planes
• Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$
• SUSY enhancement from T-branes
• An N=1 Lagrangian for the rank 1 E6 superconformal theory
• The Hasse Diagram of the Moduli Space of Instantons
• Instantons from Blow-up
• Duality Between String Junctions and D-Branes on Del Pezzo Surfaces
• Special Arithmetic of Flavor
• On 2d TQFTs whose values are holomorphic symplectic varieties
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• The Conformal Sector of F-theory GUTs
• Topological string amplitudes for the local half K3 surface
• Mixed OPEs in $\mathcal{N}=2$ Superconformal Theories
• Probing 7-branes on Orbifolds
• Infrared enhancement of supersymmetry in four dimensions
• Correlators of the Global Symmetry Currents of 4D and 6D Superconformal Theories
• On the compactification of 5d theories to 4d
• Green-Schwarz Automorphisms and 6D SCFTs
• The Higgs as a Probe of Supersymmetric Extra Sectors
• The BPS spectrum of the 4d N=2 SCFT's H_1, H_2, D_4, E_6, E_7, E_8
• Singular points in N=2 SQCD
• Kinetic Mixing at Strong Coupling
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• $\mathcal{N}=1$ conformal duals of gauged $E_n$ MN models
• 3d N=4 Bootstrap and Mirror Symmetry
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• BPS states in the Minahan-Nemeschansky E6 theory
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Quaternionic Kahler Manifolds, Constrained Instantons and the Magic Square: I
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• ADE Singularities and Coset Models
• Nilpotent Networks and 4D RG Flows
• Modular anomaly equations and S-duality in N=2 conformal SQCD
• On the BPS Spectrum of the Rank-1 Minahan-Nemeschansky Theories
• OPE coefficients in Argyres-Douglas theories
• S and T for SCFTs
• Confinement and duality in supersymmetric gauge theories
• Inozemtsev System as Seiberg-Witten Integrable system
• Hidden exceptional symmetry in the pure spinor superstring
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Lectures on 4d N=1 dynamics and related topics
• Geometric Approach to 3D Interfaces at Strong Coupling
• No go for a flow
• Supersymmetry and Strongly Coupled Gauge Theories
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Dualities of Deformed $\mathcal{N}=2$ SCFTs from Link Monodromy on D3-brane States
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• Flavor symmetries and the topology of special Kähler structures at rank 1
• Exotic Brane Junctions from F-theory
• Knots, Braids and BPS States in M-Theory
• ADE-Quiver Theories and Mirror Symmetry
• E8 Quiver Gauge Theory and Mirror Symmetry
• E-strings, $F_4$, and $D_4$ triality
• The constraining power of Coulomb Branch Geometry: lectures on Seiberg-Witten theory
• On 'categories' of quantum field theories
• Umbral Moonshine and String Duality
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• Product SCFTs for the $E_7$ Theory
• Seiberg-Witten Curve for E-String Theory Revisited
• Notes on anomalies, elliptic curves and the BS-D conjecture
• BPS index and 4d N=2 superconformal field theories
• A plethora of K3 metrics
• Families of Hitchin systems and N=2 theories
• Superconformal D-branes and moduli spaces
• Vanishing short multiplets in rank one 4d/5d SCFTs
• Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Aspects of 4d supersymmetric dynamics and geometry
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence