Renormalization group flows, the a-theorem and conformal bootstrap

Abstract

Every renormalization group flow in d spacetime dimensions can be equivalently described as spectral deformations of a generalized free CFT in (d − 1) spacetime dimensions. This can be achieved by studying the effective action of the Nambu-Goldstone boson of broken conformal symmetry in anti-de Sitter space and then taking the flat space limit. This approach is particularly useful in even spacetime dimension where the change in the Euler anomaly aUV− aIR can be related to anomalous dimensions of lowest twist multi-trace operators in the dual CFT. As an application, we provide a simple proof of the 4d a-theorem using the dual description. Furthermore, we reinterpret the statement of the a-theorem in 6d as a conformal bootstrap problem in 5d.