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.
Highlights
As quantum field theories (QFT) are subject to the renormalization group (RG) flow[1], we are naturally interested in its special points, one of which is the fixed point(s) at the end
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 ðd; pÞ, assuming that the corresponding conserved current is a conformal primary operator
Summary
As quantum field theories (QFT) are subject to the renormalization group (RG) flow[1], we are naturally interested in its special points, one of which is the fixed point(s) at the end. Fixed-point theories are scale invariant by definition, but they often enjoy even larger symmetries: gapless theories are often conformal field theories (CFT), and gapped theories are often topological quantum field theories (TQFT), where the latter include the trivially gapped theory with only one vacuum as a special case. To examine these fixed-point theories, it is useful to find some universal features of the QFT that persist along the RG flow, and it has been widely appreciated that the global symmetries and their ’t Hooft anomalies are the two prominent features. In the Appendix, we list additional constraints under the presence of supersymmetry
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