A universal result on central charges in the presence of double-trace deformations

TL;DR

This work analyzes the RG flow of large $N$ CFTs perturbed by relevant double-trace operators and proves that the IR fixed point is a CFT with the operator dimension shifted to $d-\Delta$, while UV and IR planar generating functionals are related by a Legendre transform. The authors employ the Hubbard–Stratonovich auxiliary-field technique and compute $O(1)$ corrections via a one-loop determinant on $S^d$, deriving a universal expression for the difference of Weyl anomalies $c_{IR}-c_{UV}$ that matches AdS/CFT predictions. They provide a detailed determinant calculation, handle regularization with zeta functions, and verify the result in even dimensions $d=2,4,6,8$; a complementary observation is the exact, scheme-independent expression for the two-point function at all energy scales, $Q(k)=G(k)/(1+fG(k))$, consistent with holographic results. Overall, the paper supplies a model-independent quantum-field-theoretic check of the AdS/CFT correspondence and elucidates the universality of anomaly flow under double-trace deformations.

Abstract

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.