Abstract
We revisit the classic symmetric scalar field theories in dimensions with interaction . For these theories flow to the Wilson-Fisher fixed points for any . A standard large Hubbard-Stratonovich approach also indicates that, for , these theories possess unitary UV fixed points. We propose their alternate description in terms of a theory of massless scalars with the cubic interactions and . Our one-loop calculation in dimensions shows that this theory has an IR stable fixed point at real values of the coupling constants for . We show that the expansions of various operator scaling dimensions match the known results for the critical theory continued to . These results suggest that, for sufficiently large , there are 5-dimensional unitary symmetric interacting conformal field theories (CFTs); they should be dual to the Vasiliev higher-spin theory in with alternate boundary conditions for the bulk scalar. Using these CFTs we provide a new test of the 5-dimensional theorem, and also find a new counterexample for the theorem.
1 More- Received 20 May 2014
DOI:https://doi.org/10.1103/PhysRevD.90.025018
© 2014 American Physical Society