On a CFT limit of planar γi-deformed N=4 SYM theory

We show that an integrable four-dimensional non-unitary field theory that was recently proposed as a certain limit of the gamma(i)-deformed N = 4 SYM theory is incomplete and not conformal - not even in the planar limit. We complete this theory by double-trace couplings and find conformal one-loop fixed points when admitting respective complex coupling constants. These couplings must not be neglected in the planar limit, as they can contribute to planar multi-point functions. Based on our results for certain two-loop planar anomalous dimensions, we propose tests of integrability. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.