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

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.