Remarks on compatibility between conformal symmetry and continuous higher-form symmetries

Abstract

We study the compatibility between conformal symmetry, together with unitarity, and 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.