GR from RG: Gravity Is Induced From Renormalization Group Flow In The Infrared

Abstract

In this essay and utilizing the holographic Renormalization Group (RG) flow, we demonstrate how the effective action of a non-gravitating quantum field theory in the ultraviolet (UV) develops an Einstein-Hilbert term in the infrared (IR). That is, gravity is induced by the RG flow. An inherent outcome of holography that plays a crucial role in our analysis is the \textit{RG flow of boundary conditions}: the rigid Dirichlet conditions on the background metric in the UV become an admixture of Dirichlet and Neumann as we flow to the IR, thereby ``unfreezing'' the metric and transforming it from a non-dynamical background into a dynamical field. This mechanism, which is a conceptually new addition to the standard Wilsonian RG flow, also provides the mechanism to evade the Weinberg-Witten no-go theorem. Within the GR from RG picture outlined here, the search for a quantum theory of gravity by treating the metric as a fundamental field may be a hunt for a phantom--akin to seeking the atomic structure of water by quantizing the equations of hydrodynamics.