indeed find two such lines; however, at infinite $N$ we find that $\lambda$ and $\lambda_6$ are both exactly marginal at 2-loops. In section \[allorders\] we show that this is actually true to all orders in perturbation theory, so that at infinite $N$ there is a family of conformal field theories labeled by continuous parameters $\lambda$ and $\lambda_6$. In section \[sponbreak\] we argue that there is no spontaneous breaking of the conformal symmetry in our theories.

The Beta Function $\beta_{\lambda_6}$ at Two Loops {#2loop}
--------------------------------------------------

In this section we compute $\beta_{\lambda_6}$ in momentum space using minimal subtraction. In our theory, using our dimensional reduction regularization, all 1-loop integrals are finite. Indeed, for quadratic and logarithmic divergences in three dimensions, the numerator must be an odd power of the loop momentum $q$, which must be of the form $q^\mu q^{2n}$, and then the $q$ integral vanishes by the $q\to -q$ symmetry. Linear divergences are rendered finite by dimensional regularization. In the specific case of $\beta_{\lambda_6}$, a one-loop contribution is also not allowed by the parity transformation.

Therefore, the leading contribution to this beta function arises at 2-loop order. The $\left<\phi^6\right>$ correlator (\[sixpoint\]) is superficially log-divergent, with over 50 two-loop diagrams contributing to 