  In this note, motivated by the Klebanov-Polyakov conjecture we investigate
the strongly coupled O(N) vector model at large $N$ on a squashed three-sphere
and its holographic relation to bulk gravity on asymptotically locally $AdS_4$
spaces. We present analytical results for the action of the field theory as the
squashing parameter $\alpha\to-1$, when the boundary becomes effectively one
dimensional. The dual bulk geometry is AdS-Taub-NUT space in the corresponding
limit. In this limit we solve the theory exactly and show that the action of
the strongly coupled boundary theory scales as $\ln(1+\alpha)/ (1+\alpha)^2$.
This result is remarkably close to the $-1/(1+\alpha)^2$ scaling of the
Einstein gravity action for AdS-Taub-NUT space. These results explain the
numerical agreement presented in hep-th/0503238, and the soft logarithmic
departure is interpreted as a prediction for the contribution due to higher
spin fields in the bulk $AdS_4$ geometry.
