6D SCFTs and Phases of 5D Theories

Abstract

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspondence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi--Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kahler cone of the Calabi--Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity.

v2: 45 pages, 7 figures, references and clarifications added

References in corpus (6)

• 6d Conformal Matter
• S-duality in N=2 supersymmetric gauge theories
• Holography for (1,0) theories in six dimensions
• AdS_6 solutions of type II supergravity
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• 5d/6d DE instantons from trivalent gluing of web diagrams

Cited by in corpus (74)

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• Higher Symmetries of 5d Orbifold SCFTs
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• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
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• Higher Form Symmetries TFT in 6d
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• 6D Fractional Quantum Hall Effect
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• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
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• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
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• Bootstrapping BPS spectra of 5d/6d field theories
• Dualities of 5d gauge theories from S-duality
• General Prescription for Global U(1)'s in 6D SCFTs
• Triality in Little String Theories
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• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
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• 5d/6d Wilson loops from blowups
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Rigid limit for hypermultiplets and five-dimensional gauge theories
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• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• 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
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
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• Fibre-base duality of 5d KK theories
• The Fate of Discrete 1-Form Symmetries in 6d
• Blowup Equations for Little Strings
• S-foldings of 5d SCFTs
• Generalized Toric Polygons, T-branes, and 5d SCFTs
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• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Affine characters at negative level and elliptic genera of non-critical strings
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations