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arXiv · hep-th/0611154

AdS Taub-Nut Space and the O(N) Vector Model on a Squashed 3-Sphere

Mark D. Yonge
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Abstract

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 $α\to-1$, 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 $\ln(1+α)/ (1+α)^2$. This result is remarkably close to the $-1/(1+α)^2$ 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.

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Mark D. Yonge. 2007-04-24. AdS Taub-Nut Space and the O(N) Vector Model on a Squashed 3-Sphere. https://doi.org/10.1088/1126-6708%2F2007%2F07%2F004

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