2014/04/30 by Lin Fei, Simone Giombi, Igor R. Klebanov · 1 voice · 1 citation
Physics and Astronomy · #hep-th #cond-mat.stat-mech #hep-ph
paper · pdf · doi:10.1103/physrevd.90.025018
published as Phys. Rev. D 90, 025018 (2014) · 40 pages, 8 figures. Minor corrections, references added
arxiv created 2014/08/11 · arxiv updated 2014/08/13
We revisit the classic O(N) symmetric scalar field theories in d dimensions with interaction (ϕi ϕi)2. For 2<d<4 these theories flow to the Wilson-Fisher fixed points for any N. A standard large N Hubbard-Stratonovich approach also indicates that, for 4<d<6, these theories possess unitary UV fixed points. We propose their alternate description in terms of a theory of N+1 massless scalars with the cubic interactions σϕi ϕi and σ3. Our one-loop calculation in 6-ε dimensions shows that this theory has an IR stable fixed point at real values of the coupling constants for N>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 AdS6 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 CT theorem.