\phi_i \phi_j A_\mu^a A_\mu^b
  \right. \notag\\
  &\quad \qquad \qquad \left.
  + \mu^{2\epsilon} Z_{g_6}\frac{g_6}{3!\cdot 2^3}(\phi_i\phi_i)^3
  \right\} {\,,}\label{eq:actionB}\end{aligned}$$ where $d=3-\epsilon$, and $\mu$ is the renormalization scale (for additional conventions, see Appendix \[conventions\]). The coupling $g$ is related to the integer Chern-Simons level $k$ by $k = 4\pi/g^2$. When taking the ’t Hooft large $N$ limit, the couplings $\lambda = g^2 N$ and $\lambda_6 = g_6 N^2$ are held fixed, and in this limit $\lambda$ becomes a continuous parameter. Note that while parity is broken due to the Chern-Simons interaction, the theory is dual under the combined transformation of parity plus $\lambda\to-\lambda$ ($k\to -k$), and physical results must be invariant under this transformation.

Once $\lambda > 0$, in order to renormalize the theory in a generic scheme we must add also two relevant interactions that will be generated by quantum corrections: a mass term $(\phi_i \phi_i)$ and an interaction of the form $g_4 (\phi_i \phi_i)^2$. We are interested in interacting conformal fixed points of our field theory, so we will generally fine-tune our couplings so that the physical mass and $\phi^4$ couplings vanish, and then for the purposes of our computations we can just ignore these terms. In fact, in the scheme we 