On O(N)-Symmetric Gauged $ϕ^6{}_{2+1}$ Theory with Chern-Simons Term

Abstract

I investigate the effects of the Chern-Simons coupling on high-energy behavior in $2+1$ dimensional U(1) gauged $η(ϕ^\daggerϕ)^3$ theory with a Chern-Simons term. The effective potential and the $β$ function for $η$ are calculated to the next-to-leading order of the $1/N$ expansion as functions of $θ$ (the Chern-Simons coupling). For all $θ$, the theory is found to be driven to instability region at high momenta. It is briefly discussed on radiative corrections to $θ$.