Remarks on Resonant Scalars in the AdS/CFT Correspondence

TL;DR

This paper investigates special scalar fields in AdS/CFT where their mass leads to resonant dimensions, exploring their unique properties, related anomalies, and implications for the dual conformal field theory.

Contribution

It analyzes the properties of resonant scalars in AdS/CFT, highlighting their role in trace anomalies, marginal deformations, and asymptotic charges in the gravity and dual CFT.

Findings

Resonant scalars are linked to logarithmic branches in gravity.

They are associated with trace anomalies in the CFT.

Asymptotic charges relate to properties of the dual CFT.

Abstract

The special properties of scalars having a mass such that the two possible dimensions of the dual scalar respect the unitarity and the Breitenlohner-Freedman bounds and their ratio is integral (``resonant scalars'') are studied in the AdS/CFT correspondence. The role of logarithmic branches in the gravity theory is related to the existence of a trace anomaly and to a marginal deformation in the Conformal Field Theory. The existence of asymptotic charges for the conformal group in the gravity theory is interpreted in terms of the properties of the corresponding CFT.