On Geometric Classification of 5d SCFTs

Abstract

We formulate geometric conditions necessary for engineering 5d superconformal field theories (SCFTs) via M-theory compactification on a local Calabi-Yau 3-fold. Extending the classification of the rank 1 cases, which are realized geometrically as shrinking del Pezzo surfaces embedded in a 3-fold, we propose an exhaustive classification of local 3-folds engineering rank 2 SCFTs in 5d. This systematic classification confirms that all rank 2 SCFTs predicted using gauge theoretic arguments can be realized as consistent theories, with the exception of one family which is shown to be non-perturbatively inconsistent and thereby ruled out by geometric considerations. We find that all rank 2 SCFTs descend from 6d (1,0) SCFTs compactified on a circle possibly twisted with an automorphism together with holonomies for global symmetries around the Kaluza-Klein circle. These results support our conjecture that every 5d SCFT can be obtained from the circle compactification of some parent 6d (1,0) SCFT.

66 pages + appendices. v3: Comment added concerning a rank 2 "endpoint" theory

References in corpus (4)

• 6d Conformal Matter
• Lifting 4d dualities to 5d
• Duality walls and defects in 5d N=1 theories
• Equivalence of several descriptions for 6d SCFT

Cited by in corpus (112)

• 5d Superconformal Field Theories and Graphs
• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank
• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• Higher-form symmetries of 6d and 5d theories
• Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
• Lecture Notes on Generalized Symmetries and Applications
• Trifectas for $T_N$ in 5d
• Classifying 5d SCFTs via 6d SCFTs: Rank one
• Twisted Circle Compactifications of 6d SCFTs
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• Dualities and 5-brane webs for 5d rank 2 SCFTs
• Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• Higher Symmetries of 5d Orbifold SCFTs
• Exact results for 5d SCFTs of long quiver type
• Compactification of 6d minimal SCFTs on Riemann surfaces
• 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
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Magnetic Quivers from Brane Webs with O5 Planes
• (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
• 4d $\mathcal{N}=2$ S-folds
• Revisiting the classifications of 6d SCFTs and LSTs
• Swampland Constraints on 5d $\mathcal{N}=1$ Supergravity
• Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• Flavor Symmetry of 5d SCFTs, Part 2: Applications
• Rank-3 antisymmetric matter on 5-brane webs
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Dualities of 5d gauge theories from S-duality
• Bootstrapping BPS spectra of 5d/6d field theories
• M-theoretic Genesis of Topological Phases
• Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers
• Holographic duals of five-dimensional SCFTs on a Riemann surface
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Wilson loops in 5d long quiver gauge theories
• Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Black hole microstate counting in Type IIB from 5d SCFTs
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Wilson loops in 5d $\mathcal{N}=1$ theories and S-duality
• Instantons from Blow-up
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Weakly coupled conformal manifolds in 4d
• Curious patterns of IR symmetry enhancement
• The Geometry of the SU(2)$\times$ G${}_2$-model
• Supersymmetry breaking deformations and phase transitions in five dimensions
• AdS${}_6$/CFT${}_5$ with O7-planes
• On the compactification of 5d theories to 4d
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Evidence for a 5d F-theorem
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• 5d/6d Wilson loops from blowups
• The Cat's Cradle: Deforming the higher rank $E_1$ and ${\tilde{E}}_1$ theories
• More on topological vertex formalism for 5-brane webs with O5-plane
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• The 5d Superconformal Index at Large $N$ and Black Holes
• Exploring the orthosymplectic zoo
• 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
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• Topological vertex for 6d SCFTs with ${\mathbb{Z}}_2$-twist
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• On minimal Type IIB $Ad{S}_6$ solutions with commuting 7-branes
• Twisted 6d $(2,0)$ SCFTs on a Circle
• Refined topological vertex with ON-planes
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• On non-supersymmetric fixed points in five dimensions
• Fibre-base duality of 5d KK theories
• 6d/5d exceptional gauge theories from web diagrams
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• The Fate of Discrete 1-Form Symmetries in 6d
• Linear Quivers at Large-$N$
• On the classification of 5d SCFTs
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Blowup Equations for Little Strings
• S-foldings of 5d SCFTs
• Large AdS${}_6$ black holes from CFT${}_5$
• 5d SCFTs from Decoupling and Gluing
• 5D N=1 super QFT: symplectic quivers
• Aspects of 5d Seiberg-Witten Theories on ${\mathbb{S}}^1$
• Refined topological vertex for a 5D $Sp(N)$ gauge theory with antisymmetric matter
• 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
• Symmetric Orbifold Theories from Little String Residues
• $DE$-type little strings from glued brane webs
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Compactifying 5d superconformal field theories to 3d
• 5d SCFTs and their non-supersymmetric cousins
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• B-brane transport in anomalous (2,2) models and localization
• Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions
• Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Aspects of 4d supersymmetric dynamics and geometry
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers