  The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA)
consists of a variational method which carries out a real space renormalization
scheme on the wavefunctionals of quantum field theories. In this work we
calculate the entanglement entropy of the half space for a free scalar theory
through a Gaussian cMERA circuit. We obtain the correct entropy written in
terms of the optimized cMERA variational parameter, the local density of
disentanglers. Accordingly, using the entanglement entropy production per unit
scale, we study local areas in the bulk of the tensor network in terms of the
differential entanglement generated along the cMERA flow. This result spurs us
to establish an explicit relation between the cMERA variational parameter and
the radial component of a dual AdS geometry through the Ryu-Takayanagi formula.
Finally, based on recent formulations of non-Gaussian cMERA circuits, we argue
that the entanglement entropy for the half space can be written as an integral
along the renormalization scale whose measure is given by the Fisher
information metric of the cMERA circuit. Consequently, a straightforward
relation between AdS geometry and the Fisher information metric is also
established.
