Compensating strong coupling with large charge

Abstract: We study some (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [Hellerman et al. 2015], that the effective field theory describing such sector of fixed $Q$ contains effective couplings $\lambda_{\text{eff}}\sim \lambda^b /Q^{a}$, where $\lambda$ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the $O(n)$ model in this limit.