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arXiv · 1404.1094

Critical $O(N)$ Models in $6-ε$ Dimensions

Lin Fei·Simone Giombi·Igor R. Klebanov
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Abstract

We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(ϕ^i ϕ^i)^2$. For $2 1038$. We show that the $1/N$ expansions of various operator scaling dimensions match the known results for the critical $O(N)$ theory continued to $d=6-ε$. These results suggest that, for sufficiently large $N$, there are 5-dimensional unitary $O(N)$ symmetric interacting CFT's; they should be dual to the Vasiliev higher-spin theory in AdS$_6$ with alternate boundary conditions for the bulk scalar. Using these CFT's we provide a new test of the 5-dimensional $F$-theorem, and also find a new counterexample for the $C_T$ theorem.

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Lin Fei, Simone Giombi, Igor R. Klebanov. 2014-08-11. Critical $O(N)$ Models in $6-ε$ Dimensions. https://doi.org/10.1103/physrevd.90.025018

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