In recent times we have learned that if in QFT, the constraint of locality and/or Lorentz invariance are lifted, the patterns of symmetry breaking are far richer than in local relativistic field theories. Recently we have studied some (conformal) field theories with global symmetries in the sector where the value of the global charge Q is large. We find that the low energy excitations in this sector are described by a particular form of the non-relativistic Goldstone theorem. We also provide heuristic arguments that the effective theory describing such sector contains an effective coupling constant suppressed by powers of the large charge. The comparison of our heuristic arguments with "exact" results (lattice MonteCarlo) are remarkably good.