Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States

Abstract

We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi--Yau threefolds. Field-theoretically, these 5d SCFTs descend from 6d $\mathcal{N}=(1,0)$ SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi--Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations. The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, however, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.

arXiv comment125 pages, 26 figures; v3: typos fixed

References in corpus (72)

• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• Geometric Singularities and Enhanced Gauge Symmetries
• Phase Transitions In M-Theory And F-Theory
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
• Branes, Superpotentials and Superconformal Fixed Points
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• 11-Dimensional Supergravity Compactified on Calabi-Yau Threefolds
• The D4-D8 Brane System and Five Dimensional Fixed Points
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Matter From Geometry
• On Geometric Classification of 5d SCFTs
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds
• Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
• Five-branes, Seven-branes and Five-dimensional E_n field theories
• Refined stable pair invariants for E-, M- and [p,q]-strings
• G_4 flux, chiral matter and singularity resolution in F-theory compactifications
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• Anomaly Equations and Intersection Theory
• Tate's algorithm and F-theory
• 5d quivers and their AdS(6) duals
• Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
• 6D SCFTs and Phases of 5D Theories
• M-Theory on a Calabi-Yau Manifold
• Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors
• On S-duality of 5d super Yang-Mills on S^1
• Three dimensional canonical singularity and five dimensional N=1 SCFT
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• Box Graphs and Singular Fibers
• Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
• The Tate Form on Steroids: Resolution and Higher Codimension Fibers
• Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
• Brane webs and $O5$-planes
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• Fiber-Base Duality and Global Symmetry Enhancement
• A new 5d description of 6d D-type minimal conformal matter
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• Classifying 5d SCFTs via 6d SCFTs: Rank one
• Fibrations in CICY Threefolds
• Dualities and 5-brane webs for 5d rank 2 SCFTs
• Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Duality and enhancement of symmetry in 5d gauge theories
• tt* Geometry in 3 and 4 Dimensions
• Brane webs, $5d$ gauge theories and $6d$ $\mathcal{N}$$=(1,0)$ SCFT's
• The frozen phase of F-theory
• F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• Singular del Pezzo surfaces whose universal torsors are hypersurfaces
• Toric Elliptic Fibrations and F-Theory Compactifications
• Codimension-Three Bundle Singularities in F-Theory
• On the global symmetries of 6D superconformal field theories
• Discrete theta angle from an O5-plane
• Exploring 5d BPS Spectra with Exponential Networks
• 5d fixed points from brane webs and O7-planes
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces
• The Geometry of the SU(2)$\times$ G${}_2$-model
• Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
• Euler Characteristics of Crepant Resolutions of Weierstrass Models
• The Toric SO(10) F-Theory Landscape
• Tools for CICYs in F-theory
• Global tensor-matter transitions in F-theory
• Classifying Global Symmetries of 6D SCFTs
• A Note on Non-Flat Points in the $SU(5)\times U(1)$ PQ F-Theory Model

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• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
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• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
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• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Magnetic Quivers from Brane Webs with O5 Planes
• Instantons, Symmetries and Anomalies in Five Dimensions
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• 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
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• Bootstrapping BPS spectra of 5d/6d field theories
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Dualities of 5d gauge theories from S-duality
• General Prescription for Global U(1)'s in 6D SCFTs
• Wilson loops in 5d long quiver gauge theories
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
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• 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
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• On the compactification of 5d theories to 4d
• Evidence for a 5d F-theorem
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
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• The Cat's Cradle: Deforming the higher rank $E_1$ and ${\tilde{E}}_1$ theories
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Higgsing and Twisting of 6d $D_N$ gauge theories
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities
• Exploring the orthosymplectic zoo
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• Phases of five-dimensional supersymmetric gauge theories
• Twisted 6d $(2,0)$ SCFTs on a Circle
• 3d defects in 5d: RG flows and defect F-maximization
• On non-supersymmetric fixed points in five dimensions
• 6d/5d exceptional gauge theories from web diagrams
• Fibre-base duality of 5d KK theories
• Fibration structure in toric hypersurface Calabi-Yau threefolds
• The Fate of Discrete 1-Form Symmetries in 6d
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• S-foldings of 5d SCFTs
• Bootstrapping (D, D) Conformal Matter
• Blowup Equations for Little Strings
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• On the Elliptic Calabi-Yau Fourfold with Maximal $h^{1,1}$
• Symmetric Orbifold Theories from Little String Residues
• Isomorphisms of 4d N=2 SCFTs from 6d
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Compactifying 5d superconformal field theories to 3d
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory
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• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• Symmetry TFTs from String Theory
• Aspects of 4d supersymmetric dynamics and geometry