Holography as a highly efficient RG flow I: Rephrasing gravity

Understand

We investigate how the holographic correspondence can be reformulated as a generalisation of Wilsonian RG flow in a strongly interacting large $N$ quantum field theory.

• We firstly define a \textit{highly efficient RG flow} as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale -- to achieve this it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single trace operators.
• These redefinitions also absorb the contributions of the multi-trace operators to these effective Ward identities.
• Thus the background metric and external sources become effectively dynamical reproducing the dual classical gravity equations in one higher dimension.