[@deBoer:1999xf], which relates the radial ‘evolution’ in AdS to RG flows in field theories. More recently this idea has been exploited to geometrize Wilson’s concept of integrating out momentum shells to generate field theory effective actions, in terms of integrating out regions of the bulk geometry which in turn lead to effective multi-trace boundary conditions on the cut-off surface, a fixed radial slice (in some preferred foliation) in AdS [@Heemskerk:2010hk; @Faulkner:2010jy]. One of the key features of this holographic Wilsonian approach was the emergence of multi-trace deformations of the field theory even in the planar limit, consistent with field theory expectation.

A natural question in this context is what does this RG flow mean for the gravitational equations of motion? More precisely, consider the problem of integrating out radial geometric shells in Einstein gravity with negative cosmological constant (which is a consistent truncation of string theory/supergravity). One anticipates based on the standard dictionary which relates the bulk metric to the boundary energy momentum tensor to obtain a scale dependent effective action for the energy momentum tensor, containing arbitrarily high multi-traces of the stress tensor. The reason for the generation of these multi-traces is clear, once one factors in the intrinsic 