the duality above, on the field theory side; it should be possible to map any such deformation to the gravity side as well, and to utilize the extra structure that it provides to learn more about the explicit $AdS$/CFT mapping in this case. A simple way to obtain a theory that contains only the singlet sector of the $O(N)$ vector model is by coupling $N$ free scalar fields to an $O(N)$ gauge theory; since we do not want to add any dynamics of the gauge field, we should not have standard kinetic terms for the gauge fields, but we can view their action as the $k\to \infty$ limit of the $O(N)_k$ Chern-Simons gauge theory [@Giombi:2009wh].[^1] It is then natural to deform the theory by making the Chern-Simons level $k$ a finite integer; this theory has a ’t Hooft limit, controlled by a ’t Hooft coupling $\lambda \equiv 4 \pi N / k$, and at large $N$ this gives a continuous parity-breaking deformation of the original theory. On the field theory side one can then perform computations in perturbation theory in $\lambda$, and it should be possible to translate these into perturbative computations also on the gravity side, and to obtain 