Protecting the Conformal Symmetry via Bulk Renormalization on Anti deSitter Space
Abstract
The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field {\varphi} on ddimensional Minkowski spacetime is viewed as the boundary limit of a quantum field {φ} on d + 1dimensional AntideSitter 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 oneloop "fish diagram" on AdS_{4} by differential renormalization, and calculate the anomalous dimension of the composite boundary field {\varphi^2} with bulk interaction {kappa φ^4}.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 October 2011
 DOI:
 10.1007/s0022001113110
 arXiv:
 arXiv:1003.5451
 Bibcode:
 2011CMaPh.307..315D
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 81T05;
 81T10;
 81T20
 EPrint:
 40 pages