Understanding the holographic principle via RG flow

This is a review of some recent works which demonstrate how the classical equations of gravity in AdS themselves hold the key to understanding their holographic origin in the form of a strongly coupled large $N$ QFT whose algebra of local operators can be generated by a few (single-trace) elements. I discuss how this can be realised by reformulating Einstein's equations in AdS in the form of a non-perturbative RG flow that further leads to a new approach towards constructing strongly interacting QFTs. In particular, the RG flow can self-determine the UV data that are otherwise obtained by solving classical gravity equations and demanding that the solutions do not have naked singularities. For a concrete demonstration, I focus on the hydrodynamic limit in which case this RG flow connects the AdS/CFT correspondence with the membrane paradigm, and also reproduces the known values of the dual QFT transport coefficients.