Sequences of $6d$ SCFTs on generic Riemann surfaces

Abstract

We consider compactifications of $6d$ minimal $(D_{N+3},D_{N+3})$ type conformal matter SCFTs on a generic Riemann surface. We derive the theories corresponding to three punctured spheres (trinions) with three maximal punctures, from which one can construct models corresponding to generic surfaces. The trinion models are simple quiver theories with $\mathcal{N}=1$ $SU(2)$ gauge nodes. One of the three puncture non abelian symmetries is emergent in the IR. The derivation of the trinions proceeds by analyzing RG flows between conformal matter SCFTs with different values of $N$ and relations between their subsequent reductions to $4d$. In particular, using the flows we first derive trinions with two maximal and one minimal punctures, and then we argue that collections of $N$ minimal punctures can be interpreted as a maximal one. This suggestion is checked by matching the properties of the $4d$ models such as `t Hooft anomalies, symmetries, and the structure of the conformal manifold to the expectations from $6d$. We then use the understanding that collections of minimal punctures might be equivalent to maximal ones to construct trinions with three maximal punctures, and then $4d$ theories corresponding to arbitrary surfaces, for $6d$ models described by two $M5$ branes probing a ${\mathbb{Z}}_k$ singularity. This entails the introduction of a novel type of maximal puncture. Again, the suggestion is checked by matching anomalies, symmetries and the conformal manifold to expectations from six dimensions. These constructions thus give us a detailed understanding of compactifications of two sequences of six dimensional SCFTs to four dimensions.

arXiv comment57 pages, 27 figures, v3: anomaly notations improved (see footnote 3)

References in corpus (55)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• N=2 dualities
• An Index for 4 dimensional Super Conformal Theories
• The Exact Superconformal R-Symmetry Maximizes a
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• 6d Conformal Matter
• Exact Superpotentials, Quantum Vacua and Duality in Supersymmetric SP(N_c) Gauge Theories
• Bootstrapping the superconformal index with surface defects
• On Geometric Classification of 5d SCFTs
• Anomaly polynomial of general 6d SCFTs
• Sicilian gauge theories and N=1 dualities
• N=1 Deformations and RG Flows of N=2 SCFTs
• Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• 5d Superconformal Field Theories and Graphs
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• Top Down Approach to 6D SCFTs
• Dual Boundary Conditions in 3d SCFT's
• Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank
• Tinkertoys for the Twisted D-Series
• Superconformal indices for N=1 theories with multiple duals
• The superconformal index of N=1 class S fixed points
• More on 5d descriptions of 6d SCFTs
• Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
• A new 5d description of 6d D-type minimal conformal matter
• Classifying 5d SCFTs via 6d SCFTs: Rank one
• A "Lagrangian" for a non-Lagrangian theory
• Lifting 4d dualities to 5d
• An E7 Surprise
• E-String Theory on Riemann Surfaces
• 6d SCFTs, 5d Dualities and Tao Web Diagrams
• D-type Conformal Matter and SU/USp Quivers
• Compactification of 6d minimal SCFTs on Riemann surfaces
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Compactifications of ADE conformal matter on a torus
• Fission, Fusion, and 6D RG Flows
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• Self-Dual N=1 SUSY Gauge Theories
• Charting Class ${\mathcal{S}}_k$ Territory
• Equivalence of several descriptions for 6d SCFT
• N=1 conformal dualities
• A "Lagrangian" for the E7 Superconformal Theory
• From 6d flows to 4d flows
• Surface defects and elliptic quantum groups
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Curious patterns of IR symmetry enhancement
• On the torus compactifications of $Z_2$ orbifolds of E-string theories
• Surface defects as transfer matrices
• E_8 orbits of IR dualities
• Chiral Compactifications of 6D Conformal Theories
• A freely generated ring for N=1 models in class S_k
• Punctures and Dynamical Systems

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• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
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• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
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• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
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• Rank $Q$ E-String on Spheres with Flux
• Aspects of 4d supersymmetric dynamics and geometry