Comments on compatibility between Conformal symmetry and Continuous higher-form symmetries

TL;DR

This work investigates how conformal symmetry and unitarity constrain continuous higher-form (p-form) symmetries in d-dimensional CFTs. By analyzing the unitarity bounds for conserved p-form currents and requiring the currents to be conformal primaries, the authors derive a no-go theorem stating that unitary CFTs cannot realize certain forbidden p-form symmetries, with special cases where currents decompose into chiral components. They apply these constraints to several dynamical models—free compact scalars, free Maxwell theory, a four-derivative Maxwell theory in 6d, QED in 4d, and a QED-like variant in 6d—highlighting how UV/IR fixed points and RG flows must respect the compatibility conditions, often forcing scale-invariant but non-conformal behavior or non-unitarity in the UV. The results sharpen the landscape of permissible IR behaviors and UV completions in the presence of higher-form symmetries, providing concrete checks and constraints for theorists examining conformal and topological aspects of QFTs.

Abstract

We study the compatibility between the conformal symmetry together with the unitarity and the continuous higher-form symmetries. We show that the d-dimensional unitary conformal field theories are not consistent with continuous p-form symmetries for certain (d,p), assuming that the corresponding conserved current is a conformal primary operator. We further discuss several dynamical applications of this constraint.