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Near-Conformal Dynamics at Large Charge

We investigate four-dimensional near-conformal dynamics by means of the large-charge limit. We first introduce and justify the formalism in which near-conformal invariance is insured by adding a dilaton and then determine the large-charge spectrum of the theory. The dilaton can also be viewed as the radial mode of the EFT. We calculate the two-point functions of charged operators. We discover that the mass of the dilaton, parametrising the near-breaking of conformal invariance, induces a novel term that is logarithmic in the charge. One can therefore employ the large-charge limit to explore near-conformal dynamics and determine dilaton-related properties.