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

TL;DR

This paper investigates the compatibility of conformal symmetry, unitarity, and continuous higher-form symmetries in d-dimensional conformal field theories, revealing constraints on their coexistence.

Contribution

It demonstrates that unitary conformal field theories cannot have certain continuous p-form symmetries, assuming the conserved current is a conformal primary.

Findings

Certain (d,p) combinations are incompatible with unitarity and conformal symmetry.

Provides constraints applicable to dynamical models in conformal field theory.

Highlights the role of primary operators in symmetry compatibility.

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.