Instantons, Symmetries and Anomalies in Five Dimensions

Abstract

All five-dimensional non-abelian gauge theories have a $U(1{)}_I$ global symmetry associated with instantonic particles. We describe an obstruction to coupling $U(1{)}_I$ to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed 't Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.

28 pages; v2: references and some comments added

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• Higher Symmetries of 5d Orbifold SCFTs
• Continuous Generalized Symmetries in Three Dimensions
• Higher Form Symmetries TFT in 6d
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
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• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Zero-form and one-form symmetries of the ABJ and related theories
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
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• Phases of five-dimensional supersymmetric gauge theories
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
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• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Monopole Breaking of Chern-Weil Symmetries
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• Compactifying 5d superconformal field theories to 3d
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• 5d SCFTs and their non-supersymmetric cousins
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
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• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview