CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
The dilaton Wess-Zumino action in higher dimensions
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abstract
We present a general formula for the Wess-Zumino action associated with the Weyl anomaly, given in a curved background for any even number of dimensions. The result is obtained by considering a finite Weyl transformation of counterterms in dimensional regularization.
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Moduli Spaces in CFT: Large Charge Operators
CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.