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2019

Renormalization Group Flows, the $a$-Theorem and Conformal Bootstrap

Kundu, Sandipan

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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_{UV}-a_{IR}$ 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.

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