AdS Taub-NUT space and the O(N) vector model on a squashed 3-sphere

In this note, motivated by the Klenbanov-Polyakov conjective 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 locall AdS(4) spaces. We present analyst results for the action of the field theory as the squashing paramenter alpha -> -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.