Holographic renormalisation group ows and renormalisation from a Wilsonian perspective Lizana, J. M. Morris, T. R. Pérez-Victoria Moreno De Barreda, Manuel María AdS-CFT Correspondence Gauge-gravity correspondence Renormalization Group From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular xed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satis ed by the Wilson action and nd the corresponding xed points and their eigendeformations, which have a diagonal evolution close to the xed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss di erent renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group ows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space. 2024-10-16T11:21:37Z 2024-10-16T11:21:37Z 2016-03-30 journal article Lizana, J.M. & Morris, T.R. & Pérez Victoria Moreno de Barreda, M.M. J. High Energ. Phys. 2016, 198 (2016). [https://doi.org/10.1007/JHEP03(2016)198] https://hdl.handle.net/10481/96022 10.1007/JHEP03(2016)198 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer