Erratum to: Scaling dimensions of monopole operators in the ℂ ℙ N b − 1 $$ \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^{N_b-1} $$ theory in 2 + 1 dimensions

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.