Renormalization group flows, the \(a \)-theorem and conformal bootstrap

DOI10.1007/JHEP05(2020)014zbMATH Open1437.81058arXiv1912.09479OpenAlexW3102361440MaRDI QIDQ779292

Author name not available (Why is that?)

Publication date: 21 July 2020

Published in: (Search for Journal in Brave)

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

a_{U V} - a_{I R}

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.

Full work available at URL: https://arxiv.org/abs/1912.09479

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