  Using holography, we study the entanglement entropy of strongly coupled field
theories perturbed by operators that trigger an RG flow from a conformal field
theory in the ultraviolet (UV) to a new theory in the infrared (IR). The
holographic duals of such flows involve a geometry that has the UV and IR
regions separated by a transitional structure in the form of a domain wall. We
address the question of how the geometric approach to computing the
entanglement entropy organizes the field theory data, exposing key features as
the change in degrees of freedom across the flow, how the domain wall acts as a
UV region for the IR theory, and a new area law controlled by the domain wall.
Using a simple but robust model we uncover this organization, and expect much
of it to persist in a wide range of holographic RG flow examples. We test our
formulae in two known examples of RG flow in 3+1 and 2+1 dimensions that
connect non-trivial fixed points.
