Monopoles in CPN-1 model via the state-operator correspondence

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 CP1 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 CPN-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.