minimum of the effective potential at $\sigma=0$. Thus, at least for weak couplings and large $N$, the conformal symmetry is not spontaneously broken in the two-parameter family of conformal field theories that we discussed above. For $\lambda=0$ a spontaneous breaking of the conformal symmetry can occur when $\lambda_6 = (4\pi)^2$ exactly, and it would be interesting to investigate how this statement is modified at finite $\lambda$ (see [@Dias:2003pw; @Dias:2010it] for a study of the effective potential in the Abelian Chern-Simons-Matter theory, and [@Rabinovici:2011jj] for a similar study of the $O(N)$ vector model with a Chern-Simons term for a $U(1)$ subgroup of $O(N)$). For small values of $N$, spontaneous breaking of the conformal symmetry might happen (as in [@Ferrari:2010ex]), and it would be interesting to check if it happens in our theories.

Higher-Spin Currents {#HScurrents}
====================

The main goal of this section is to find the spectrum of primary operators of the large $N$ interacting fixed points discovered in the previous section. Let us begin by considering the free theory, taking $\lambda=\lambda_6=0$. For each positive, even spin $s$ it has a unique $O(N)$-singlet primary operator $J_s$ that saturates the unitarity bound $\Delta \ge s + d - 2$. (In the theory 