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

TL;DR

This paper derives a universal formula for the change in central charges in large N conformal field theories undergoing double-trace deformations, confirming the results with AdS/CFT predictions and providing a scheme-independent two-point function calculation.

Contribution

It presents a universal expression for the difference in scale anomalies between UV and IR fixed points in large N CFTs with double-trace deformations, validated by field theory and holography.

Findings

Universal formula for scale anomaly difference

Agreement with AdS/CFT predictions

Scheme-independent two-point function computation

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.