An Effective Theory for Holographic RG Flows

TL;DR

This paper develops a holographic effective field theory for RG flows, deriving the dilaton action and anomalies in various dimensions, and verifies anomaly distinctions using Gauss-Bonnet terms.

Contribution

It introduces a bulk effective theory for the Goldstone boson of broken spacetime symmetry in holography, enabling computation of dilaton actions and anomalies across dimensions.

Findings

Computed dilaton actions in 2D and higher dimensions.

Verified anomaly differentiation using Gauss-Bonnet terms.

Established a holographic EFT framework for RG flows.

Abstract

We study the dilaton action induced by RG flows between holographic CFT fixed points. For this purpose we introduce a general bulk effective theory for the goldstone boson of the broken spacetime symmetry, providing an AdS analog of the EFT of Inflation. In two dimensions, we use the effective theory to compute the dilaton action, as well as the UV and IR conformal anomalies, without further assumptions. In higher dimensions we take a `slow-flow' limit analogous to the assumption of slow-roll in Inflation, and in this context we obtain the dilaton action, focusing on terms proportional to the difference of the A-type anomalies. We include Gauss-Bonnet terms in the gravitational action in order to verify that our method correctly differentiates between A-type and other anomalies.