Protecting the conformal symmetry via bulk renormalization on Anti deSitter space

TL;DR

This paper investigates how bulk renormalization in Anti-de Sitter space can preserve conformal symmetry at the boundary, avoiding anomalies and providing explicit calculations of key diagrams and anomalous dimensions.

Contribution

It demonstrates that boundary conformal symmetry can be maintained through bulk renormalization, with explicit computations showing the absence of anomalies and calculating anomalous dimensions.

Findings

No conformal anomaly when boundary limit exists

Explicit calculation of the fish diagram on AdS_4

Determination of anomalous dimension of boundary field

Abstract

The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi^2 with bulk interaction Phi^4.