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

TL;DR

This paper studies how the Chern-Simons coupling influences the high-energy behavior of a 2+1 dimensional gauged $ ext{phi}^6$ theory, revealing that the theory becomes unstable at high momenta regardless of the coupling strength.

Contribution

It provides the first calculation of the effective potential and beta function for the theory with a Chern-Simons term at next-to-leading order in 1/N expansion, highlighting the universal instability.

Findings

The theory is driven to instability at high momenta for all values of the Chern-Simons coupling.

The effective potential and beta function depend explicitly on the Chern-Simons coupling parameter.

Radiative corrections to the Chern-Simons coupling are briefly discussed.

Abstract

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