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

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.

arXiv comment14 pages, 5 tables

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• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• B-brane transport in anomalous (2,2) models and localization
• Higher-form anomalies and state-operator correspondence beyond conformal invariance