Monopoles inCPN−1model via the state-operator correspondence

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One of the earliest proposed phase transitions beyond the Landau-Ginzburg-Wilson paradigm is the quantum critical point separating an antiferromagnet and a valence-bond solid on a square lattice. The low-energy description of this transition is believed to be given by the $2+1$ dimensional ${\text{CP}}^{1}$ model---a theory of bosonic spinons coupled to an Abelian gauge field. Monopole defects of the gauge field play a prominent role in the physics of this phase transition. In the present paper, we use the state-operator correspondence of conformal field theory in conjunction with the $1/N$ expansion to study monopole operators at the critical fixed point of the ${\text{CP}}^{N\ensuremath{-}1}$ model. This elegant method reproduces the result for monopole scaling dimension obtained through a direct calculation by Murthy and Sachdev. The technical simplicity of our approach makes it the method of choice when dealing with monopole operators in a conformal field theory.