Scaling dimensions of monopole operators in the $\mathbb{CP}^{N_b - 1}$ theory in $2+1$ dimensions

TL;DR

This paper calculates the scaling dimensions of monopole operators in the 2+1 dimensional $ ext{CP}^{N_b - 1}$ theory at criticality, using analytical methods and confirming results with numerical lattice studies.

Contribution

It provides the next-to-leading order analytical computation of monopole operator dimensions in the $ ext{CP}^{N_b - 1}$ theory, aligning with numerical findings in quantum antiferromagnets.

Findings

Analytical scaling dimensions match numerical lattice results.

Next-to-leading order corrections improve previous estimates.

Monopole operators correspond to valence bond solid order parameters.

Abstract

We study monopole operators at the conformal critical point of the $\mathbb{CP}^{N_b - 1}$ theory in $2+1$ spacetime dimensions. Using the state-operator correspondence and a saddle point approximation, we compute the scaling dimensions of these operators to next-to-leading order in $1/N_b$. We find remarkable agreement between our results and numerical studies of quantum antiferromagnets on two-dimensional lattices with SU($N_b$) global symmetry, using the mapping of the monopole operators to valence bond solid order parameters of the lattice antiferromagnet.