2006/11/30 by Mark D. Yonge, Mark Duke Yonge
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1088/1126-6708/2007/07/004
published as JHEP0707:004,2007 · 11 pages, 3 figures. References added
arxiv created 2007/04/24 · openalex publication_date 2007/07/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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 AdS4 spaces. We present analytical results for the action of the field theory as the squashing parameter α→-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 AdS4 geometry.