Compensating strong coupling with large charge

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 [1], that the effective field theory describing such sector of fixed Q contains effective couplings lambda(eff) similar to 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.