Dualities of 5d gauge theories from S-duality

Abstract

We describe a general method to determine dualities between supersymmetric 5d gauge theories. The method is based on performing local S-dualities in the geometry associated to the gauge theory. We find that often a duality can be obtained by adding matter to both sides of a more primitive duality. This allows us to define the notion of irreducible dualities which cannot be obtained from more primitive dualities. More general dualities then are obtained by adding matter to both sides of an irreducible duality. The geometric method described in this paper allows us to systematically construct irreducible dualities. As an application, we explicitly determine a special class of irreducible dualities classified by removal and addition of edges into a Dynkin diagram. This class of dualities vastly generalizes many of the known 5d dualities in the literature.

arXiv comment137 pages, v2: References added, v3: List of dualities relevant for 5d gauge theory descriptions of 5d SCFTs and 6d SCFTs added, v4: Corrected typos pointed out by Sakura Schafer-Nameki and Brian Willett, v5: Minor typos corrected

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Cited by in corpus (24)

• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Higher-form symmetries of 6d and 5d theories
• 2-Group Symmetries of 6d Little String Theories and T-duality
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• Twisted Circle Compactifications of 6d SCFTs
• (5d RG-flow) Trees in the Tropical Rain Forest
• Classification of 5d N=1 gauge theories
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• Flavor Symmetry of 5d SCFTs, Part 2: Applications
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities
• On non-supersymmetric fixed points in five dimensions
• Fibre-base duality of 5d KK theories
• Linear Quivers at Large-$N$
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• Aspects of 4d supersymmetric dynamics and geometry