Holographic Wilsonian RG Flow and Sliding Membrane Paradigm

Understand

We study the relations between two different approaches to the holographic Renormalization Group (RG) flow at the dual gravity level: One is the radial evolution of the classical equation of motion and the other is the flow equation given by the holographic Wilsonian RG coming from the cut off independence.

• Apparently, the two flows look different.
• We give general proofs that the two flows are actually equivalent.
• The role of the momentum continuity (MC) is essential.