Gravity Is Induced By Renormalization Group Flow

Abstract: We revisit the holographic renormalization group (RG) setting in which a 4-dimensional ($4d$) quantum field theory at a finite cutoff corresponds to/is described by the Einstein gravity on a part of AdS$_{5}$ space, cutoff at a finite radius. This holographic setting has interesting and important implications for the $4d$ field theory: Deformation of the field theory by a certain combination involving the square of its energy-momentum tensor can be alternatively viewed as formulating the field theory on a background with a dynamical metric. Explicitly, starting with a non-gravitating $4d$ field theory in the UV, flowing to the IR, quantum effects that we compute using the classical $5d$ Einstein gravity theory, induce an effective $4d$ Einstein gravity theory. In other words, we show that gravity is not a fundamental force and is an effective description of quantum effects in the IR limit.