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We study monopole operators at the conformal critical point of the \( \mathbb{C}{\mathrm{\mathbb{P}}}^{N_b-1} \) theory in 2+1 spacetime dimensions. Using the state-operator correspondence and a saddle point approximation, we compute the scaling dimensions of the operators that insert one or two units of magnetic flux to next-to-leading order in 1/N  b . We compare our results to 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. For the monopole operators that insert three or more units of magnetic flux, we find that the rotationally-symmetric saddle point is unstable; in order to obtain the scaling dimensions of these operators, even at leading order in 1/N  b , one should consider non-spherically-symmetric saddles.

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