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

arXiv comment29 pages + Appendices, 3 figures; v2 corrected an important minus sign error and made various improvements