Critical O (N) models in 6-ε dimensions

We revisit the classic O(N) symmetric scalar field theories in d dimensions with interaction (φiφi)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 σφiφi 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 conformal field theories (CFTs); they should be dual to the Vasiliev higher-spin theory in AdS6 with alternate boundary conditions for the bulk scalar. Using these CFTs we provide a new test of the 5-dimensional F theorem, and also find a new counterexample for the CT theorem.