Holographic Renormalisation and Anomalies

The Weyl anomaly in the Holographic Renormalisation Group as implemented using Hamilton–Jacobi language is studied in detail. We investigate the breakdown of the descent equations in order to isolate the Weyl anomaly of the dual field theory close to the (UV) fixed point. We use the freedom of adding finite terms to the renormalised effective action in order to bring the anomalies in the expected form. We comment on different ways of describing the bare and renormalised schemes, and on possible interpretations of the descent equations as describing the renormalisation group flow non-perturbatively. We find that under suitable assumptions these relations may lead to a class of c-functions. E-mail addresses: [email protected] (J. K.), [email protected] (D. M.), [email protected] (W. M.)