Monopoles in CP(N-1) model via the state-operator correspondence

TL;DR

This paper employs the state-operator correspondence and 1/N expansion to analyze monopole operators at the critical point of the CP(N-1) model, confirming previous results with a simpler method.

Contribution

It introduces a straightforward conformal field theory approach to compute monopole scaling dimensions in the CP(N-1) model, simplifying prior calculations.

Findings

Reproduces known monopole scaling dimensions using a new method

Demonstrates the effectiveness of the state-operator correspondence in this context

Provides a simpler computational framework for monopole operators

Abstract

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 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 CP(N-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.