are using (of dimensional reduction and minimal subtraction), once we fix the renormalized dimensionful couplings to zero, they remain zero so we do not even have to add them to our action.

At least in the large $N$ limit, we could also study the theory in which the coupling $g_4$ does not vanish; if it is non-zero then the theory flows to another fixed point, which at large $N$ is closely related to the original fixed point (at infinite $N$ it has the same spectrum of operators, except for the operator $\phi_i \phi_i$ whose dimension at the interacting fixed point is $\Delta=2$). For the theory with $\lambda=0$ this was discussed in the $AdS$/CFT context in [@Klebanov:2002ja; @Gubser:2002vv; @Petkou:2003zz; @Giombi:2011ya], and the same analysis holds also at finite $\lambda$. Therefore, most of our results also apply to the “critical” fixed point with a non-zero $g_4$ coupling. However, for simplicity, we will focus here on the case where the physical $g_4$ coupling is tuned to vanish.

Note that dimensional regularization of this theory is subtle, since the 3-form integration of the Chern-Simons interaction (\[eq:actionCS\]) is not well-defined for arbitrary dimension. To regulate loop integrals we first perform the tensor algebra in 3 