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.
Highlights
Space with finite but large radius RAdS and take the flat space limit RAdS → ∞
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 approach is 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
Summary
In this paper we will mainly focus on RG flows between conformal fixed points in 6d. We will comment on some aspects of 4d RG flows throughout the paper. The trace of the stress tensor for 6d CFTs is anomalous in the presence of a background metric. Central charges c(i) appear in the stress tensor. Three-point function and they are constrained by the conformal collider bounds [39]. There are no constraints on the Euler central charge a since it only contributes to the stress tensor four-point function. The claim that the Euler central charge is a measure of the effective number of degrees of freedom is slightly stronger than the a-theorem in 6d
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