The large charge expansion at large N

TL;DR

This paper numerically verifies the universal large charge behavior of scaling dimensions of monopole operators in a 2+1 dimensional CPN model, confirming theoretical predictions with high precision.

Contribution

It provides the first numerical verification of the universal large charge expansion in the 2+1 dimensional CPN model, including subleading order terms.

Findings

Universal O(1) contribution confirmed to subpercent accuracy

Scaling dimensions computed for charges Q=1 to 100

Large Q expansion coefficients extracted and verified

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.