Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics

TL;DR

This paper computes the anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics using a perturbative $1/N_f$ expansion, providing more precise results than previous leading order calculations.

Contribution

It advances the understanding of monopole operator dimensions by calculating next-to-leading order corrections in the $1/N_f$ expansion.

Findings

Scaling dimension of the $n=1$ monopole operator is approximately 0.265 N_f minus 0.0383 at the IR fixed point.

Provides improved theoretical predictions for monopole operator dimensions in 3D QED.

Enhances the accuracy of operator scaling dimensions beyond leading order in the $1/N_f$ expansion.

Abstract

The space of local operators in three-dimensional quantum electrodynamics contains monopole operators that create $n$ units of gauge flux emanating from the insertion point. This paper uses the state-operator correspondence to calculate the anomalous dimensions of these monopole operators perturbatively to next-to-leading order in the $1/N_f$ expansion, thus improving on the existing leading order results in the literature. Here, $N_f$ is the number of two-component complex fermion flavors. The scaling dimension of the $n=1$ monopole operator is $0.265 N_f - 0.0383 + O(1/N_f)$ at the infrared conformal fixed point.