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

M. M. Sheikh-Jabbari, V. Taghiloo

TL;DR

The work proposes that gravity is not fundamental but emergent from the IR dynamics of a non-gravitational UV theory via holographic RG flow. By relating radial evolution in AdS to the RG flow of the boundary action, the authors derive a TT-driven flow that induces the Einstein-Hilbert term and a cosmological constant, with running couplings $\kappa_4(\mu)$, $\Lambda_4(\mu)$, and $\beta(\mu)$. The boundary-condition RG flow further unfreezes the metric, enabling a dynamical 4D geometry, and holographic renormalization yields a renormalized action with $\Lambda_4^{\text{ren}}=0$ and scale-invariant $\kappa_4^{\text{ren}}$, addressing the cosmological constant and non-renormalizability issues. The framework also explains how the Weinberg-Witten no-go theorem is evaded and motivates revisiting Wilsonian RG in the presence of dynamical spacetime, positioning gravity as a collective IR phenomenon akin to hydrodynamics rather than a fundamental UV field.

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.

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

TL;DR

The work proposes that gravity is not fundamental but emergent from the IR dynamics of a non-gravitational UV theory via holographic RG flow. By relating radial evolution in AdS to the RG flow of the boundary action, the authors derive a TT-driven flow that induces the Einstein-Hilbert term and a cosmological constant, with running couplings , , and . The boundary-condition RG flow further unfreezes the metric, enabling a dynamical 4D geometry, and holographic renormalization yields a renormalized action with and scale-invariant , addressing the cosmological constant and non-renormalizability issues. The framework also explains how the Weinberg-Witten no-go theorem is evaded and motivates revisiting Wilsonian RG in the presence of dynamical spacetime, positioning gravity as a collective IR phenomenon akin to hydrodynamics rather than a fundamental UV field.

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.
Paper Structure (8 sections, 9 equations, 1 figure)

This paper contains 8 sections, 9 equations, 1 figure.

Table of Contents

  1. Quest for Quantum Gravity
  2. GR From (Holographic) RG
  3. Computing the boundary effective action $S^{\text{bdy}}_{\Sigma(r)}$ at the RG scale $r/L^2$.
  4. RG Flow of Boundary Conditions
  5. Concluding Remarks
  6. Renormalized Bulk Theory.
  7. How do we evade Weinberg-Witten No-Go Theorem?
  8. Deviation from the standard Wilsonian RG.

Figures (1)

  • Figure 1: Visualization of the emergence of dynamical gravity. The inner surface $\Sigma(r)$ represents the cutoff hypersurface at the renormalization scale $r$. The irregular, distorted grid is to stress the fact that the metric on $\Sigma(r)$, $\gamma_{ab}(r)$, is a dynamical fluctuating field. Its dynamics is governed by the RG flow of boundary conditions discussed in section \ref{['sec:RG-bcs']}.