Irrelevant Operators and their Holographic Anomalies

Irrelevant operators in a CFT modify the usual Weyl transformation of the metric. A metric beta-function turns on, which modifies the Weyl anomalies as well. In this paper, we study the relation between bulk diffeomorphisms and Weyl transformation at the boundary when a massive scalar field, which sources irrelevant operators at the boundary, is coupled to the bulk metric. Considering the effect of the backreaction generated by the scalar field, we provide a holographic description of the boundary metric beta-function and anomalies. Our results represent an additional test of the AdS/CFT correspondence.Comment: 19 pages + appendices, matches published version; added references, more comments on the results and added appendix with the complete expression of the anomaly; Mathematica notebook with explicit results, including the anomaly, attache