The large charge expansion at large N

Abstract

The scaling dimensions of charged operators in conformal field theory have recently been predicted to exhibit universal behavior in the large charge limit. We verify this behavior in the 2+1 dimensional CPN model. Specifically, we numerically compute the scaling dimensions of the lowest dimension monopole operators with charges Q = 1, 2, ... , 100 to subleading order in large N. The coefficients of the large Q expansion are extracted through a fit, and the predicted universal O(1) contribution is verified to the subpercent level.