Protecting the conformal symmetry via bulk renormalization on Anti deSitter space

Michael Dütsch, Karl-Henning Rehren
March 29, 2010
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 ${\rm AdS}_4$ by differential renormalization, and calculate the anomalous dimension of the composite boundary field $\phi^2$ with bulk interaction $\Phi^4$.