Anomalous Magnetic Moment of Anyons in three dimensional $CP^{N-1}$ Model

TL;DR

This paper computes the anomalous magnetic moment of anyons in a 3D $CP^{N-1}$ model with a Chern-Simons term, revealing that infinite-mass anyons have a $g$-factor of 2 and that certain interactions are attractive.

Contribution

It provides a detailed $1/N$ expansion analysis of the $g$-factor for anyons in the $CP^{N-1}$ model, confirming the exact value of 2 for infinite-mass anyons and exploring interaction regimes.

Findings

$g$-factor of infinite-mass anyons is 2 up to next-to-leading order

Electromagnetic interactions are attractive for certain $ heta$ ranges

Supports the claim that nonrelativistic anyons have $g=2"

Abstract

We calculate the anomalous magnetic moment of anyons in three dimensional $CP^{N-1}$ model with a Chern-Simons term in various limits in $1/N$ expansion. We have found that for anyons of infinite mass the gyromagnetic ratio ($g$-factor) is 2 up to the next-to-leading order in $1/N$. Our result supports a recent claim that the $g$-factor of nonrelativistic anyons is exactly two. We also found that for $-{8\over\pi }<\theta<0$, the electromagnetic interation between two identical aynons of large mass are attractive.