Critical O(N) models in 6-epsilon dimensions

Abstract

We revisit the classic O(N) symmetric scalar field theories in d dimensions with interaction (phi(i)phi(i))(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 sigma phi(i)phi(i) and sigma(3). Our one-loop calculation in 6 - epsilon 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 - epsilon. 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 AdS(6) 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 C-T theorem.