Gravity Is Not a Fundamental Force: Renormalization Group Flow Induced Gravity

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 AdS5 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.