5d Superconformal Field Theories and Graphs

Abstract

We propose a graph-theoretic description to determine and characterize 5d superconformal field theories (SCFTs) that arise as circle reductions of 6d $\mathcal{N}=(1,0)$ SCFTs. Each 5d SCFT is captured by a graph, called a Combined Fiber Diagram (CFD). Transitions between CFDs encode mass deformations that trigger flows between SCFTs. In this way, the complete set of descendants of a given 6d theory are obtained from a single marginal CFD. The graphs encode key physical information like the superconformal flavor symmetry and BPS states. As an illustration, we ascertain the aforementioned data associated to all the 5d SCFTs descending from 6d minimal $(E_6,E_6)$ and $(D_k,D_k)$ conformal matter for any $k$. This includes predictions for thus far unknown flavor symmetry enhancements.

6 pages, 2 figures. Supplementary material available here: https://people.maths.ox.ac.uk/schafernamek/CFD

References in corpus (10)

• 5-dim Superconformal Index with Enhanced En Global Symmetry
• On Geometric Classification of 5d SCFTs
• Refined stable pair invariants for E-, M- and [p,q]-strings
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• Three dimensional canonical singularity and five dimensional N=1 SCFT
• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
• Dualities and 5-brane webs for 5d rank 2 SCFTs
• Duality and enhancement of symmetry in 5d gauge theories
• Towards Classification of 5d SCFTs: Single Gauge Node

Cited by in corpus (72)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• Higher-form symmetries of 6d and 5d theories
• Lecture Notes on Generalized Symmetries and Applications
• Trifectas for $T_N$ in 5d
• Twisted Circle Compactifications of 6d SCFTs
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• 2-Group Symmetries and M-Theory
• Higher Symmetries of 5d Orbifold SCFTs
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• (5d RG-flow) Trees in the Tropical Rain Forest
• Classification of 5d N=1 gauge theories
• Magnetic Quivers from Brane Webs with O5 Planes
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
• 4d $\mathcal{N}=2$ S-folds
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study
• Flavor Symmetry of 5d SCFTs, Part 2: Applications
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Bootstrapping BPS spectra of 5d/6d field theories
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• Dualities of 5d gauge theories from S-duality
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions
• Fibrations and Hasse diagrams for 6d SCFTs
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Non-Simply-Connected Symmetries in 6D SCFTs
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Weakly coupled conformal manifolds in 4d
• AdS${}_6$/CFT${}_5$ with O7-planes
• Supersymmetry breaking deformations and phase transitions in five dimensions
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
• 5d/6d Wilson loops from blowups
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• On the compactification of 5d theories to 4d
• Evidence for a 5d F-theorem
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Genus zero Gopakumar-Vafa invariants from open strings
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• The Cat's Cradle: Deforming the higher rank $E_1$ and ${\tilde{E}}_1$ theories
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities
• Higgsing and Twisting of 6d $D_N$ gauge theories
• Phases of five-dimensional supersymmetric gauge theories
• Twisted 6d $(2,0)$ SCFTs on a Circle
• On non-supersymmetric fixed points in five dimensions
• Fibre-base duality of 5d KK theories
• 6d/5d exceptional gauge theories from web diagrams
• On the classification of 5d SCFTs
• The Fate of Discrete 1-Form Symmetries in 6d
• Bootstrapping (D, D) Conformal Matter
• Blowup Equations for Little Strings
• S-foldings of 5d SCFTs
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• Generating functions for intersection products of divisors in resolved F-theory models
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Isomorphisms of 4d N=2 SCFTs from 6d
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Aspects of 4d supersymmetric dynamics and geometry
• Symmetry TFTs from String Theory
• On holographic duals of certain isolated weighted Gorenstein cDV singularities