Compensating strong coupling with large charge (東京)

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 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 that the effective field theory describing such sector of fixed $Q$ contains effective couplings $\lambda_{\rm{eff}}\sim \lambda^b /Q^{a}$, 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.