that it depends on $\lambda$. We end in section \[summary\] with a summary of our results and a discussion of some future directions.

The $O(N)$ Model with Chern-Simons Interactions {#On}
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Consider the theory of a real scalar field $\phi$ in the fundamental representation of $O(N)$, coupled to gauge bosons $A_\mu$ with Chern-Simons interactions at level $k$ in three Euclidean dimensions (the generalization to $N$ complex scalar fields coupled to a $U(N)_k$ Chern-Simons theory is straightforward, and we will occasionally discuss below this case as well). We regulate the theory using dimensional reduction [@Siegel:1979wq] (see below), and work in Lorenz gauge (Landau gauge), $\partial^{\mu}A_\mu=~0$. The regularized action in terms of the renormalized fields and couplings is $$\begin{aligned}
  S &= S_\mathrm{CS} + S_\mathrm{gh} + S_\mathrm{b}{\,,}\label{eq:action}\\
  S_\mathrm{CS} &= \int \! d^dx\, \left\{
  - \frac{i}{2} Z_A
  \epsilon_{\mu\nu\lambda} A_\mu^a \partial_\nu A_\lambda^a
  - \frac{i}{6} \mu^{\epsilon/2} g Z_g \epsilon_{\mu\nu\lambda} f^{abc}
  A_\mu^a A_\nu^b A_\lambda^c
  \right\}{\,,}\label{eq:actionCS}\\
    S_\mathrm{gh} &= \int \! d^dx\, \left\{
  - \frac{1}{2 \gamma_R} (\partial_\mu A_\mu^a)^2
  + Z_\mathrm{gh} \partial_\mu \bar{c}^a \partial^\mu c^a
  + \mu^{\epsilon/2} \tilde{Z}_g g f^{abc}
  \partial_\mu \bar{c}^a A_\mu^b c^c
  \right\}{\,,}\label{eq:actionGH}\\
    S_\mathrm{b} &= \int \! d^dx\, \left\{
  \frac{1}{2} Z_\phi (\partial_\mu \phi_i)^2
  + \mu^{\epsilon/2} Z_g' g \partial_\mu \phi_i T_{ij}^a
  A_\mu^a \phi_j
  - \frac{1}{4} \mu^\epsilon Z_g'' g^2 \{T^a,T^b\}_{ij}
    