E-String Theory on Riemann Surfaces

Abstract

We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dimensions. In particular we identify N=1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E_8 flavor symmetry. This sheds light on emergent symmetries in a number of 4d N=1 SCFTs (including the `E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries.

85 pages, 25 figures, harvmac

References in corpus (45)

• Heterotic and Type I String Dynamics from Eleven Dimensions
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Eleven-Dimensional Supergravity on a Manifold with Boundary
• N=2 dualities
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• An Index for 4 dimensional Super Conformal Theories
• Small Instantons in String Theory
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• The Exact Superconformal R-Symmetry Maximizes a
• Phase Transitions In M-Theory And F-Theory
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Comments on String Dynamics in Six Dimensions
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Gauge Theories and Macdonald Polynomials
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• S-duality in N=2 supersymmetric gauge theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Superconformal Fixed Points with E_n Global Symmetry
• S-duality and 2d Topological QFT
• Four-Dimensional SCFTs from M5-Branes
• Bootstrapping the superconformal index with surface defects
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• Sicilian gauge theories and N=1 dualities
• Exactly Marginal Deformations and Global Symmetries
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• Holography for (1,0) theories in six dimensions
• Supersymmetric Index In Four-Dimensional Gauge Theories
• E-Strings and N=4 Topological Yang-Mills Theories
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• On S-duality of 5d super Yang-Mills on S^1
• Superconformal indices for N=1 theories with multiple duals
• The superconformal index of N=1 class S fixed points
• Anomaly polynomial of E-string theories
• A "Lagrangian" for a non-Lagrangian theory
• An E7 Surprise
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• Charting Class ${\mathcal{S}}_k$ Territory
• Non-trivial flat connections on the 3-torus I: G_2 and the orthogonal groups
• Non-trivial flat connections on the 3-torus II: The exceptional groups F_4 and E_6,7,8
• $\mathcal{N}=1$ superconformal theories with $D_N$ blocks
• Chiral Compactifications of 6D Conformal Theories

Cited by in corpus (65)

• 5d Partition Functions with A Twist
• 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
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Rank $Q$ E-string on a torus with flux
• Compactifications of ADE conformal matter on a torus
• Revisiting the classifications of 6d SCFTs and LSTs
• AdS${}_7$/CFT${}_6$ with orientifolds
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• 4D Gauge Theories with Conformal Matter
• Anomalies, Black strings and the charged Cardy formula
• Defect $a$-Theorem and $a$-Maximization
• N=1 conformal dualities
• A slow review of the AGT correspondence
• From 6d flows to 4d flows
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• M-theoretic Genesis of Topological Phases
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• A tale of exceptional 3d dualities
• 't Hooft anomalies and boundaries
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• An N=1 Lagrangian for the rank 1 E6 superconformal theory
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Weakly coupled conformal manifolds in 4d
• Curious patterns of IR symmetry enhancement
• Between symmetry and duality in supersymmetric QFT
• On the torus compactifications of $Z_2$ orbifolds of E-string theories
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• E-string Quantum Curve
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• Star shaped quivers with flux
• Flips, dualities and symmetry enhancements
• On the 3d compactifications of 5d SCFTs associated with SU(N+1) gauge theories
• Symmetry enhancement and duality walls in 5d gauge theories
• $\mathcal{N}=1$ conformal duals of gauged $E_n$ MN models
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Elliptic Quantum Curves of 6d SO(N) theories
• Star shaped quivers in four dimensions
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking
• Fibre-base duality of 5d KK theories
• Non minimal D-type conformal matter compactified on three punctured spheres
• Nilpotent Networks and 4D RG Flows
• A freely generated ring for N=1 models in class S_k
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• 4d N=1 from 6d D-type N=(1,0)
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Compactifying 5d superconformal field theories to 3d
• The Geometry of Decoupling Fields
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• E-strings, $F_4$, and $D_4$ triality
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Rank $Q$ E-String on Spheres with Flux
• Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions
• Aspects of 4d supersymmetric dynamics and geometry
• Computing distances on Riemann surfaces