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arxiv: 2602.11806 · v2 · pith:EYXOM7LOnew · submitted 2026-02-12 · ✦ hep-th · astro-ph.CO· gr-qc· hep-ph

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

M.M. Sheikh-Jabbari , V. Taghiloo This is my paper

Pith reviewed 2026-05-21 13:41 UTC · model grok-4.3

classification ✦ hep-th astro-ph.COgr-qchep-ph
keywords holographic RG flowinduced gravityEinstein-Hilbert termboundary conditionsemergent gravityWeinberg-Witten no-go theorem
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The pith

Holographic RG flow induces the Einstein-Hilbert term in the infrared.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that the effective action for a quantum field theory without gravity in the ultraviolet acquires an Einstein-Hilbert term in the infrared via holographic renormalization group flow. The mechanism relies on the evolution of boundary conditions that unfreezes the metric. A sympathetic reader would care because this frames gravity as an induced phenomenon from RG flow, suggesting that fundamental quantization of the metric may not be the right path.

Core claim

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 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标准ly

What carries the argument

The RG flow of boundary conditions, shifting from rigid Dirichlet to an admixture of Dirichlet and Neumann, which unfreezes the metric and renders it dynamical.

If this is right

  • The IR effective action includes an Einstein-Hilbert term.
  • The metric transforms from a non-dynamical background to a dynamical field.
  • The Weinberg-Witten no-go theorem is evaded through the flowing boundary conditions.
  • Treating the metric as fundamental for quantum gravity is like quantizing hydrodynamic equations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This view reframes the problem of quantum gravity as finding appropriate UV QFTs rather than quantizing GR directly.
  • It may connect to other approaches where gravity emerges at long distances.
  • Testable in principle by computing IR actions in concrete holographic examples.

Load-bearing premise

The RG flow in the holographic setup causes the boundary conditions to evolve from rigid Dirichlet to a Dirichlet-Neumann admixture.

What would settle it

An explicit computation of the IR effective action in a holographic model that shows the presence or absence of a generated Einstein-Hilbert term.

Figures

Figures reproduced from arXiv: 2602.11806 by M.M. Sheikh-Jabbari, V. Taghiloo.

Figure 1
Figure 1. Figure 1: Visualization of the emergence of dynamical gravity. The inner surface Σ(r) represents the cutoff hyper￾surface at the renormalization scale r. The irregular, distorted grid is to stress the fact that the metric on Σ(r), γab(r), is a dynamical fluctuating field. Its dynamics is governed by the RG flow of boundary conditions discussed in section 3. metric from a static/fixed UV background into a dynamical f… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that, via holographic renormalization group flow, the effective action of a non-gravitating UV quantum field theory develops an Einstein-Hilbert term in the IR. Gravity is thereby induced purely by the RG flow. A central mechanism is the RG flow of boundary conditions on the metric, which evolves from rigid Dirichlet in the UV to a mixed Dirichlet-Neumann admixture in the IR; this 'unfreezes' the metric, renders it dynamical, and evades the Weinberg-Witten theorem. The search for quantum gravity by quantizing the metric is likened to quantizing hydrodynamics.

Significance. If the central claim is made rigorous with explicit derivations, the work would offer a conceptually novel route to emergent gravity in which the metric arises as an IR degree of freedom generated by RG flow rather than being fundamental. It extends holographic RG ideas by emphasizing boundary-condition flow as a new ingredient and could reframe quantum-gravity searches away from direct metric quantization. The absence of free parameters in the stated axioms is a potential strength, but the result remains conceptual until quantitative checks are supplied.

major comments (2)
  1. [Abstract] Abstract and opening paragraphs: the central claim that an Einstein-Hilbert term is generated in the IR effective action is stated conceptually but without an explicit derivation, action, or coefficient computation. The manuscript must supply a concrete calculation (e.g., the one-loop or holographic effective action expansion) demonstrating that the EH coefficient arises from the RG flow itself rather than being inserted by hand or inherited from the bulk gravitational action.
  2. [Abstract] Abstract, paragraph on 'RG flow of boundary conditions': the transition from rigid Dirichlet to mixed Dirichlet-Neumann boundary conditions is presented as an inherent outcome of holography that unfreezes the metric. Because standard holographic RG already assumes a bulk Einstein gravity theory whose on-shell action reproduces the boundary effective action, an explicit demonstration is required that this boundary-condition flow (and the resulting EH term) can be obtained from a purely non-gravitational UV QFT without presupposing the bulk gravitational dynamics. A concrete test would be a field-theoretic computation of the induced metric two-point function that matches the EH propagator independently of the bulk action.
minor comments (2)
  1. The manuscript is framed as an 'essay'; adding at least one explicit example (e.g., a specific CFT or lattice model) with numerical or analytic verification of the induced EH coefficient would strengthen the presentation without altering the conceptual scope.
  2. Notation for the mixed boundary conditions should be defined more precisely (e.g., the relative weight between Dirichlet and Neumann components as a function of the RG scale) to allow readers to reproduce the unfreezing argument.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading and constructive suggestions. We address each major comment point by point below, indicating the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract and opening paragraphs: the central claim that an Einstein-Hilbert term is generated in the IR effective action is stated conceptually but without an explicit derivation, action, or coefficient computation. The manuscript must supply a concrete calculation (e.g., the one-loop or holographic effective action expansion) demonstrating that the EH coefficient arises from the RG flow itself rather than being inserted by hand or inherited from the bulk gravitational action.

    Authors: We agree that an explicit derivation would make the central claim more rigorous. The present manuscript is an essay that outlines the conceptual mechanism. In the revised version we will add a dedicated section sketching the holographic effective action obtained by integrating the radial flow equations with evolving boundary conditions. This will show explicitly how the Einstein-Hilbert coefficient is fixed by the RG scale rather than being inserted by hand. revision: yes

  2. Referee: [Abstract] Abstract, paragraph on 'RG flow of boundary conditions': the transition from rigid Dirichlet to mixed Dirichlet-Neumann boundary conditions is presented as an inherent outcome of holography that unfreezes the metric. Because standard holographic RG already assumes a bulk Einstein gravity theory whose on-shell action reproduces the boundary effective action, an explicit demonstration is required that this boundary-condition flow (and the resulting EH term) can be obtained from a purely non-gravitational UV QFT without presupposing the bulk gravitational dynamics. A concrete test would be a field-theoretic computation of the induced metric two-point function that matches the EH propagator independently of the bulk action.

    Authors: The UV starting point is a non-gravitational QFT with a fixed, non-dynamical metric. The holographic RG flow is the Wilsonian integration of high-momentum modes; as the radial cutoff is lowered, the boundary conditions on the metric necessarily evolve from Dirichlet to a mixed Dirichlet-Neumann form. This evolution is dictated by the requirement of a well-defined variational principle at each scale and does not presuppose IR gravity. We will revise the text to state this logic more explicitly and to contrast it with the standard fixed-boundary holographic dictionary. A complete, non-holographic field-theoretic computation of the metric two-point function lies outside the scope of the present conceptual work. revision: partial

standing simulated objections not resolved
  • A fully independent, non-holographic field-theoretic calculation of the induced metric two-point function that reproduces the Einstein-Hilbert propagator without any reference to bulk dynamics.

Circularity Check

1 steps flagged

Holographic RG setup presupposes bulk gravity, so claimed induction of EH term reduces to re-expressing the gravitational dual

specific steps
  1. other [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 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-dynamica"

    The demonstration relies on holographic RG, whose definition already incorporates a bulk gravitational theory whose on-shell action induces the boundary effective action (including the EH term). The 'unfreezing' via boundary-condition flow is likewise an outcome of the same holographic dictionary rather than an independent RG mechanism starting from a purely non-gravitational UV QFT.

full rationale

The paper's derivation begins by invoking holographic RG flow on a non-gravitating UV QFT to generate an IR Einstein-Hilbert term and a flow of boundary conditions from rigid Dirichlet to mixed Dirichlet-Neumann. This mechanism is presented as an inherent outcome of holography that unfreezes the metric. However, standard holographic RG is defined within a bulk gravitational theory (typically Einstein gravity in AdS), so the boundary effective action and metric dynamics are inherited from the bulk action via the duality dictionary rather than generated purely by field-theoretic RG evolution of a non-gravitational theory. The central claim therefore reduces to the input holographic assumption.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard holographic correspondence and introduces the RG flow of boundary conditions as the load-bearing new element; no explicit free parameters or new entities are named in the abstract.

axioms (2)
  • domain assumption Holographic duality relating a non-gravitational QFT to a gravitational theory in one higher dimension
    Invoked throughout the abstract as the framework that makes the RG flow analysis possible.
  • ad hoc to paper RG flow of boundary conditions from rigid Dirichlet to mixed Dirichlet-Neumann
    Presented as an inherent outcome of holography that is crucial for unfreezing the metric.

pith-pipeline@v0.9.0 · 5732 in / 1528 out tokens · 61733 ms · 2026-05-21T13:41:55.997734+00:00 · methodology

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Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · 23 internal anchors

  1. [1]

    Grumiller and M

    D. Grumiller and M. M. Sheikh-Jabbari,Black Hole Physics: From Collapse to Evaporation. Grad.Texts Math. Springer, 11, 2022

    work page 2022

  2. [2]

    The quantum structure of spacetime at the Planck scale and quantum fields

    S. Doplicher, K. Fredenhagen, and J. E. Roberts, “The Quantum structure of space-time at the Planck scale and quantum fields,”Commun. Math. Phys.172(1995) 187–220, hep-th/0303037

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  3. [3]

    The Large N Limit of Superconformal Field Theories and Supergravity

    J. M. Maldacena, “The largeNlimit of superconformal field theories and supergravity,”Adv. Theor. Math. Phys.2(1998) 231–252,hep-th/9711200

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  4. [4]

    Black holes and entropy,

    J. D. Bekenstein, “Black holes and entropy,”Phys. Rev.D7(1973) 2333–2346

    work page 1973

  5. [5]

    Particle Creation by Black Holes,

    S. W. Hawking, “Particle Creation by Black Holes,”Commun. Math. Phys.43(1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    work page 1975

  6. [6]

    Thermodynamics of Spacetime: The Einstein Equation of State

    T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,”Phys. Rev. Lett.75(1995) 1260–1263,gr-qc/9504004

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  7. [7]

    Thermodynamical Aspects of Gravity: New insights

    T. Padmanabhan, “Thermodynamical Aspects of Gravity: New insights,”Rept. Prog. Phys. 73(2010) 046901,0911.5004. 11

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  8. [8]

    Nonlinear Fluid Dynamics from Gravity

    S. Bhattacharyya, V . E. Hubeny, S. Minwalla, and M. Rangamani, “Nonlinear Fluid Dynamics from Gravity,”JHEP02(2008) 045,0712.2456

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  9. [9]

    On the Origin of Gravity and the Laws of Newton

    E. P. Verlinde, “On the Origin of Gravity and the Laws of Newton,”JHEP04(2011) 029, 1001.0785

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  10. [10]

    Cool horizons for entangled black holes

    J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,”Fortsch. Phys.61 (2013) 781–811,1306.0533

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  11. [11]

    Holographic Derivation of Entanglement Entropy from AdS/CFT

    S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,”Phys.Rev.Lett.96(2006) 181602,hep-th/0603001

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  12. [12]

    Building up spacetime with quantum entanglement,

    M. Van Raamsdonk, “Building up spacetime with quantum entanglement,”Gen. Rel. Grav. 42(2010) 2323–2329,1005.3035. [Int. J. Mod. Phys.D19,2429(2010)]

    work page arXiv 2010

  13. [13]

    Addendum to Computational Complexity and Black Hole Horizons

    L. Susskind, “Computational Complexity and Black Hole Horizons,”Fortsch. Phys.64 (2016) 24–43,1403.5695. [Addendum: Fortsch.Phys. 64, 44–48 (2016)]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  14. [14]

    Vacuum quantum fluctuations in curved space and the theory of gravitation,

    A. D. Sakharov, “Vacuum quantum fluctuations in curved space and the theory of gravitation,”Dokl. Akad. Nauk Ser. Fiz.177(1967) 70–71

    work page 1967

  15. [15]

    Gravity Is Induced By Renormalization Group Flow,

    H. Adami, M. M. Sheikh-Jabbari, and V . Taghiloo, “Gravity Is Induced By Renormalization Group Flow,”2508.09633

    work page arXiv

  16. [16]

    Anti De Sitter Space And Holography

    E. Witten, “Anti-de Sitter space and holography,”Adv. Theor. Math. Phys.2(1998) 253–291,hep-th/9802150

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  17. [17]

    Large N Field Theories, String Theory and Gravity

    O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y . Oz, “Large N field theories, string theory and gravity,”Phys. Rept.323(2000) 183–386,hep-th/9905111

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  18. [18]

    The Holographic Bound in Anti-de Sitter Space

    L. Susskind and E. Witten, “The holographic bound in anti-de Sitter space,” hep-th/9805114. 12

    work page internal anchor Pith review Pith/arXiv arXiv

  19. [19]

    UV/IR Relations in AdS Dynamics

    A. W. Peet and J. Polchinski, “UV/IR relations in AdS dynamics,”Phys. Rev. D59(1999) 065011,hep-th/9809022

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  20. [20]

    On the Holographic Renormalization Group

    J. de Boer, E. P. Verlinde, and H. L. Verlinde, “On the holographic renormalization group,” JHEP08(2000) 003,hep-th/9912012

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  21. [21]

    Quantum effective action from the AdS/CFT correspondence

    K. Skenderis and S. N. Solodukhin, “Quantum effective action from the AdS/CFT correspondence,”Phys. Lett.B472(2000) 316–322,hep-th/9910023

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  22. [22]

    Lecture Notes on Holographic Renormalization

    K. Skenderis, “Lecture notes on holographic renormalization,”Class. Quant. Grav.19 (2002) 5849–5876,hep-th/0209067

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  23. [23]

    Quasilocal energy and conserved charges derived from the gravitational action,

    J. D. Brown and J. W. York, Jr., “Quasilocal energy and conserved charges derived from the gravitational action,”Phys. Rev.D47(1993) 1407–1419

    work page 1993

  24. [24]

    Holography at finite cutoff with a $T^2$ deformation

    T. Hartman, J. Kruthoff, E. Shaghoulian, and A. Tajdini, “Holography at finite cutoffwith a T 2 deformation,”JHEP03(2019) 004,1807.11401

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  25. [25]

    Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence,

    A. Parvizi, M. M. Sheikh-Jabbari, and V . Taghiloo, “Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence,”2503.09372

    work page arXiv

  26. [26]

    Moving the CFT into the bulk with $T\bar T$

    L. McGough, M. Mezei, and H. Verlinde, “Moving the CFT into the bulk withT T,”JHEP 04(2018) 010,1611.03470

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  27. [27]

    TT deformations in general dimensions

    M. Taylor, “T ¯Tdeformations in general dimensions,”Adv. Theor. Math. Phys.27(2023), no. 1, 37–63,1805.10287

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  28. [28]

    On space of integrable quantum field theories

    F. A. Smirnov and A. B. Zamolodchikov, “On space of integrable quantum field theories,” Nucl. Phys. B915(2017) 363–383,1608.05499

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    Gravity in Warped Compactifications and the Holographic Stress Tensor

    S. de Haro, K. Skenderis, and S. N. Solodukhin, “Gravity in warped compactifications and the holographic stress tensor,”Class. Quant. Grav.18(2001) 3171–3180, hep-th/0011230. 13

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  30. [30]

    Holographic and Wilsonian Renormalization Groups

    I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,” JHEP06(2011) 031,1010.1264

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  31. [31]

    Beyond Space-Time

    A. M. Polyakov, “Beyond space-time,”hep-th/0602011

    work page internal anchor Pith review Pith/arXiv arXiv

  32. [32]

    The hydrodynamic approach to quantum gravity,

    T. Banks, “The hydrodynamic approach to quantum gravity,”Int. J. Mod. Phys. D34 (2025), no. 16, 2544020,2505.15941

    work page arXiv 2025

  33. [33]

    Limits on Massless Particles,

    S. Weinberg and E. Witten, “Limits on Massless Particles,”Phys.Lett.B96(1980) 59. 14

    work page 1980