$CP^N$ Model With a Chern-Simons Term

TL;DR

This paper investigates the $CP^N$ model in three dimensions with a Chern-Simons term, showing the CS coefficient's beta function is zero at leading order and likely all orders, affecting the model's critical behavior.

Contribution

It provides an explicit calculation of the beta function for the Chern-Simons coefficient and argues its vanishing to all orders in the $1/N$ expansion.

Findings

Beta function for the CS coefficient is zero at order 1/N.

The beta function is argued to be zero to all orders.

Remarks on the impact of $ heta$ on critical exponents.

Abstract

The $CP^N$ model in three euclidean dimensions is studied in the presence of a Chern-Simons term using the $1/N$ expansion. The $\beta$-function for the CS coefficient $\theta$ is found to be zero to order $1/N$ in the unbroken phase by an explicit calculation. It is argued to be zero to all orders. Some remarks on the $\theta$ dependence of the critical exponents are also made.