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Recently proposed double trace deformations of large $N$ holographic CFTs infour dimensions define a one parameter family of quantum field theories, whichare interpreted in the bulk dual as living on successive finite radiushypersurfaces. The transformation of variables that turns the equation definingthe deformation of a four dimensional large $N$ CFT by such operators into theexpression for the radial ADM Hamiltonian in the bulk is found.  This prescription clarifies the role of various functions of backgroundfields that appear in the flow equation defining the deformed holographic CFT,and also their relationship to the holographic anomaly.  The effect of these deformations can also be seen as triggering a generalizedgradient flow for the fields of the induced gravity theory obtained fromintegrating out the fundamental fields of the holographic CFT. The potentialfor this gradient flow is found to resemble the two derivative effective actionpreviously derived using holographic renormalization.

Finite Cutoff AdS$_{5}$ Holography and the Generalized Gradient Flow