  We study large N conformal field theories perturbed by relevant double-trace
deformations. Using the auxiliary field trick, or Hubbard-Stratonovich
transformation, we show that in the infrared the theory flows to another CFT.
The generating functionals of planar correlators in the ultraviolet and
infrared CFT's are shown to be related by a Legendre transform. Our main result
is a universal expression for the difference of the scale anomalies between the
ultraviolet and infrared fixed points, which is of order 1 in the large N
expansion. Our computations are entirely field theoretic, and the results are
shown to agree with predictions from AdS/CFT. We also remark that a certain
two-point function can be computed for all energy scales on both sides of the
duality, with full agreement between the two and no scheme dependence.
