Comments on Global Symmetries and Anomalies of $5d$ SCFTs

TL;DR

The paper investigates how global symmetries, including 1-form and higher-form structures, constrain five-dimensional SCFTs and their RG flows. It shows that mixed anomalies between instantonic and 1-form symmetries limit the faithful flavor groups and constrain RG trajectories, and it analyzes anomaly matching in the E1 SCFT and in 3d N=4 SQED as guiding examples. It argues that conformal invariance disfavors unbroken continuous 1-form symmetries in 5d, implying spontaneous breaking or decoupled sectors, and explores the implications for 2-group symmetries. Finally, it uses anomaly considerations to sharpen proposed UV dualities in supersymmetric 5d RG flows, demonstrating that mismatch of IR anomalies can rule out certain IR gauge theories as dual descriptions of the same UV fixed point.

Abstract

We study various aspects of global symmetries in five-dimensional superconformal field theories. Whenever a supersymmetry-preserving relevant deformation is available, the infrared gauge theory description might exhibit a finite order mixed 't Hooft anomaly between a $1$-form symmetry and the instantonic symmetry. This anomaly constrains the flavor symmetry group acting faithfully on the SCFT and the consistency of certain RG flows. As an additional example, we consider the instructive case of three-dimensional $\mathcal{N}=4$ SQED. Finally, we discuss the compatibility between conformal invariance and the presence of $1$-form and $2$-group global symmetries.