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arxiv: 2606.27333 · v1 · pith:5GAJ7SQHnew · submitted 2026-06-25 · ✦ hep-th

The IKKT renormalization group flow is IIB: toward zero-d holography

Xiangwen Guan , Joel Karlsson , S\'ebastien Reymond , Thomas Van Riet This is my paper

Pith reviewed 2026-06-26 02:15 UTC · model grok-4.3

classification ✦ hep-th
keywords IKKT matrix modelD-instantonsrenormalization group flowholographyaxio-dilatontype IIB supergravityCoulomb branch
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The pith

The BZJ renormalization flow on the IKKT matrix model makes the coupling run with rank N to match the axio-dilaton in IIB supergravity.

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

The paper develops a holographic map for D-instantons in the IKKT matrix model, which lacks ordinary spacetime. It applies the Brézin-Zinn-Justin renormalization group flow to the partition function, causing the effective coupling g to run with matrix rank N. This running exactly reproduces the N-dependence of the axio-dilaton field that appears in the supergravity solution for a stack of D-instantons. The construction first uses integration over heavy strings in a Coulomb branch vacuum to relate the leading correction coefficient to the string coupling, then extends the same logic through the full BZJ flow that also integrates Coulomb branch positions. The result supplies a zero-dimensional version of the running-coupling holography already known for higher-dimensional Dp-branes.

Core claim

Applying the BZJ-flow to the IKKT partition function leads to a running of the coupling constant g with the rank N of the matrix model, reproducing the N-dependence of the axio-dilaton field in supergravity.

What carries the argument

The Brézin-Zinn-Justin matrix renormalization group flow applied to the IKKT model, which integrates out both heavy modes and Coulomb branch positions to produce an effective running coupling.

If this is right

  • The IKKT model supplies a holographic description of D-instanton stacks whose dilaton profile is reproduced by the matrix RG flow.
  • The string coupling extracted from the leading correction term acquires a position dependence on the Coulomb branch that agrees with supergravity.
  • The same flow provides a matrix realization of the running dilaton for the p=-1 case, extending the pattern known for p greater than or equal to 0.

Where Pith is reading between the lines

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

  • Similar RG flows could be defined on other matrix models to derive candidate holographic duals for different brane stacks.
  • Numerical evaluation of the flowed IKKT partition function might produce concrete predictions for correlation functions that can be compared with supergravity.
  • The method may extend to include higher-order corrections or additional fields beyond the axio-dilaton.

Load-bearing premise

The coefficient of the leading correction to the IKKT action can be identified with the string coupling and the Coulomb branch integration method applies to the D-instanton case.

What would settle it

A direct computation of the N-dependence of g from the BZJ flow on the IKKT partition function that fails to reproduce the N-dependence of the axio-dilaton in the corresponding D-instanton supergravity solution would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.27333 by Joel Karlsson, S\'ebastien Reymond, Thomas Van Riet, Xiangwen Guan.

Figure 1
Figure 1. Figure 1: FIG. 1. An illustration of the two stacks of D [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

Supergravity solutions describing stacks of D$p$-branes with $p\neq 3$ feature a non-constant dilaton profile, which is holographically mapped to the running of the SYM coupling in $(p+1)$ dimensions. For D-instantons ($p=-1$), the lack of space and time in the IKKT matrix model makes such an interpretation difficult at first. In this letter, we propose a method to achieve this based on two closely related concepts: the IKKT method of integrating out heavy strings in a Coulomb branch vacuum and the matrix RG flow of Br\'ezin and Zinn-Justin (BZJ). The notable difference between the two is that the BZJ RG flow also integrates over the Coulomb branch position. We first apply the Coulomb branch method and by relating the coefficient of the leading correction to the IKKT action with the string coupling, we can compute its dependence on the Coulomb branch position, finding a match between matrix theory and supergravity. Next, we apply the BZJ-flow to the IKKT partition function, which leads to a running of the coupling constant $g$ with the rank $N$ of the matrix model, reproducing the $N$-dependence of the axio-dilaton field in supergravity.

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

1 major / 0 minor

Summary. The paper claims that applying the Coulomb branch integration method to the IKKT matrix model for D-instantons, after identifying the coefficient of the leading correction to the action with the string coupling, yields a position-dependent match to the supergravity axio-dilaton; subsequently applying the Brézin-Zinn-Justin RG flow to the IKKT partition function produces a running of the coupling g with matrix rank N that reproduces the N-dependence of the axio-dilaton in supergravity.

Significance. If the identification and flow steps are placed on a first-principles footing, the result would supply a concrete matrix-model derivation of holographic running in zero dimensions and strengthen the link between IKKT and type IIB supergravity.

major comments (1)
  1. [Abstract] Abstract (final two paragraphs): the central claim requires that the prefactor of the leading correction obtained by integrating out heavy strings on the Coulomb branch equals the string coupling (rather than an arbitrary function of the eigenvalues). No intermediate calculation or first-principles argument for this identification is supplied; without it the subsequent reproduction of the supergravity N-dependence via BZJ flow is an assumption, not a derivation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for highlighting this important point regarding the identification step. We address the comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final two paragraphs): the central claim requires that the prefactor of the leading correction obtained by integrating out heavy strings on the Coulomb branch equals the string coupling (rather than an arbitrary function of the eigenvalues). No intermediate calculation or first-principles argument for this identification is supplied; without it the subsequent reproduction of the supergravity N-dependence via BZJ flow is an assumption, not a derivation.

    Authors: We agree that the identification of the prefactor with the string coupling is central and that the manuscript would benefit from a clearer statement of its motivation. This identification is introduced because the leading correction term generated by Coulomb-branch integration must be matched to the known position-dependent axio-dilaton of the D-instanton supergravity solution; once made, the subsequent BZJ flow reproduces the N-dependence without further tuning. In the revised manuscript we will expand both the abstract and the introductory discussion to spell out this matching requirement explicitly and to note that the identification is the minimal choice consistent with the holographic dictionary for p = -1. We acknowledge that a complete first-principles derivation of the prefactor from the IKKT action alone lies beyond the scope of the present letter and remains an open question. revision: partial

Circularity Check

1 steps flagged

Identification of leading correction coefficient with string coupling forces reproduction of axio-dilaton N-dependence via BZJ flow

specific steps
  1. fitted input called prediction [Abstract]
    "by relating the coefficient of the leading correction to the IKKT action with the string coupling, we can compute its dependence on the Coulomb branch position, finding a match between matrix theory and supergravity. Next, we apply the BZJ-flow to the IKKT partition function, which leads to a running of the coupling constant g with the rank N of the matrix model, reproducing the N-dependence of the axio-dilaton field in supergravity."

    The reproduction of the N-dependence is obtained only after the coefficient is related/identified with the string coupling g; the BZJ flow then converts that N-dependent g into the claimed supergravity profile. The output is therefore the input identification renamed as a prediction.

full rationale

The paper's central claim reduces to an identification step that is then fed into the BZJ flow. The abstract explicitly states that the match and the subsequent N-running are obtained after 'relating the coefficient of the leading correction to the IKKT action with the string coupling'. This makes the claimed reproduction of the supergravity N-dependence a direct consequence of the chosen identification rather than an independent first-principles output. No equations are shown that derive the coefficient equaling the string coupling without that relation. The derivation is therefore partially circular at the load-bearing identification step.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that the Coulomb branch integration correctly captures the string coupling dependence and that the BZJ flow can be applied directly to the IKKT partition function; no explicit free parameters or new entities are named in the abstract.

free parameters (1)
  • identification of leading correction coefficient with string coupling
    The mapping between the matrix-model correction term and the string coupling is introduced to obtain the position dependence.
axioms (2)
  • domain assumption Coulomb branch method applies to integrating out heavy strings in the IKKT model for D-instantons
    Invoked to compute the dependence on Coulomb branch position and relate it to supergravity.
  • domain assumption BZJ RG flow can be applied to the IKKT partition function to extract running with N
    Used to obtain the N-dependence that is then compared to supergravity.

pith-pipeline@v0.9.1-grok · 5766 in / 1436 out tokens · 23551 ms · 2026-06-26T02:15:26.123343+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

35 extracted references · 1 canonical work pages

  1. [1]

    A Large N reduced model as superstring,

    N. Ishibashi, H. Kawai, Y. Kitazawa, and A. Tsuchiya, “A Large N reduced model as superstring,”Nucl. Phys. B498(1997) 467–491,arXiv:hep-th/9612115

    Pith/arXiv arXiv 1997

  2. [2]

    The Weyl spinorsψhave16complex components and ψΓm[X m, ψ] =ψ α(CΓm)αβ[X m, ψβ]

    We adopt the notation[X, X]2 = [Xm, Xn][X m, Xn]. The Weyl spinorsψhave16complex components and ψΓm[X m, ψ] =ψ α(CΓm)αβ[X m, ψβ]. The convention for the fermion term is discussed in [31, 33]

  3. [3]

    Instantons and seven-branes in type IIB superstring theory,

    G. W. Gibbons, M. B. Green, and M. J. Perry, “Instantons and seven-branes in type IIB superstring theory,”Phys. Lett. B370(1996) 37–44, arXiv:hep-th/9511080

    Pith/arXiv arXiv 1996

  4. [4]

    New perspectives on the emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model,

    J. Nishimura, “New perspectives on the emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model,”PoSCORFU2019(2020) 178, arXiv:2006.00768 [hep-lat]

    arXiv 2020

  5. [5]

    Emergent metric space-time from matrix theory,

    S. Brahma, R. Brandenberger, and S. Laliberte, “Emergent metric space-time from matrix theory,” JHEP09(2022) 031,arXiv:2206.12468 [hep-th]

    arXiv 2022

  6. [6]

    H. C. Steinacker,Quantum Geometry, Matrix Theory, and Gravity. Cambridge University Press, 4, 2024

    2024

  7. [7]

    Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling,

    H. C. Steinacker, “Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling,” arXiv:2605.13294 [hep-th]

    Pith/arXiv arXiv

  8. [8]

    Holography for the Ishibashi-Kawai-Kitazawa-Tsuchiya Matrix Model,

    F. Ciceri and H. Samtleben, “Holography for the Ishibashi-Kawai-Kitazawa-Tsuchiya Matrix Model,” Phys. Rev. Lett.135no. 6, (2025) 061601, arXiv:2503.08771 [hep-th]

    arXiv 2025

  9. [9]

    Supergravity dual for Ishibashi-Kawai-Kitazawa-Tsuchiya holography,

    F. Ciceri and H. Samtleben, “Supergravity dual for Ishibashi-Kawai-Kitazawa-Tsuchiya holography,”Phys. Rev. D113no. 4, (2026) 046001,arXiv:2511.23111 [hep-th]. 8

    arXiv 2026

  10. [10]

    The matrix edge of holography,

    F. Ciceri and H. Samtleben, “The matrix edge of holography,”arXiv:2604.00355 [hep-th]

    arXiv

  11. [11]

    Renormalization group approach to matrix models,

    E. Brézin and J. Zinn-Justin, “Renormalization group approach to matrix models,”Physics Letters B288 no. 1–2, (Aug., 1992) 54–58. http://dx.doi.org/10.1016/0370-2693(92)91953-7

    work page doi:10.1016/0370-2693(92)91953-7 1992

  12. [12]

    Renormalization group approach to matrix models and vector models,

    S. Higuchi, C. Itoi, and N. Sakai, “Renormalization group approach to matrix models and vector models,” Prog. Theor. Phys. Suppl.114(1993) 53–71, arXiv:hep-th/9307154

    Pith/arXiv arXiv 1993

  13. [13]

    Random vector and matrix and vector theories: a renormalization group approach,

    J. Zinn-Justin, “Random vector and matrix and vector theories: a renormalization group approach,”J. Statist. Phys.157(2014) 990–1016,arXiv:1410.1635 [math-ph]

    Pith/arXiv arXiv 2014

  14. [14]

    Wilsonian renormalization group for a multitrace matrix model,

    B. Ydri and R. Ahmim, “Wilsonian renormalization group for a multitrace matrix model,”Int. J. Mod. Phys. A37no. 27, (2022) 2250165,arXiv:2008.09564 [hep-th]

    arXiv 2022

  15. [15]

    Revisited functional renormalization group approach for random matrices in the large-Nlimit,

    V. Lahoche and D. Ousmane Samary, “Revisited functional renormalization group approach for random matrices in the large-Nlimit,”Phys. Rev. D101no. 10, (2020) 106015,arXiv:1909.03327 [hep-th]

    arXiv 2020

  16. [16]

    Blocking up D branes: Matrix renormalization?,

    K. Narayan, “Blocking up D branes: Matrix renormalization?,”arXiv:hep-th/0211110

    Pith/arXiv arXiv

  17. [17]

    Supergravity and the large N limit of theories with sixteen supercharges,

    N. Itzhaki, J. M. Maldacena, J. Sonnenschein, and S. Yankielowicz, “Supergravity and the large N limit of theories with sixteen supercharges,”Phys. Rev. D58 (1998) 046004,arXiv:hep-th/9802042

    Pith/arXiv arXiv 1998

  18. [18]

    The domain wall / QFT correspondence,

    H. J. Boonstra, K. Skenderis, and P. K. Townsend, “The domain wall / QFT correspondence,”JHEP01 (1999) 003,arXiv:hep-th/9807137

    Pith/arXiv arXiv 1999

  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, arXiv:hep-th/9809022

    Pith/arXiv arXiv 1999

  20. [20]

    Precision holography for non-conformal branes,

    I. Kanitscheider, K. Skenderis, and M. Taylor, “Precision holography for non-conformal branes,”JHEP 09(2008) 094,arXiv:0807.3324 [hep-th]

    Pith/arXiv arXiv 2008

  21. [21]

    Correlation functions for non-conformal Dp-brane holography,

    N. Bobev, G. Mera Álvarez, and H. Paul, “Correlation functions for non-conformal Dp-brane holography,” JHEP07(2025) 137,arXiv:2503.18770 [hep-th]

    arXiv 2025

  22. [22]

    Scaling similarities and quasinormal modes of D0 black hole solutions,

    A. Biggs and J. Maldacena, “Scaling similarities and quasinormal modes of D0 black hole solutions,”JHEP 11(2023) 155,arXiv:2303.09974 [hep-th]

    arXiv 2023

  23. [23]

    A Test of the AdS / CFT duality on the Coulomb branch,

    M. S. Costa, “A Test of the AdS / CFT duality on the Coulomb branch,”Phys. Lett. B482(2000) 287–292, arXiv:hep-th/0003289. [Erratum: Phys.Lett.B 489, 439–439 (2000)]. [24]TrF 4 = 1 3 Tr(FmnF npFpqF qm) + 2 3 Tr(FmnFpqF mqF pn)− 1 6 Tr(FmnF mnFpqF pq)− 1 12 Tr(FmnFpqF mnF pq)

    Pith/arXiv arXiv 2000

  24. [24]

    Other proposals for reducing the rank have been put forward, for example averaging overM×Msub-blocks such thatN→N/M[16]

  25. [25]

    D instantons and matrix models,

    P. Vanhove, “D instantons and matrix models,”Class. Quant. Grav.16(1999) 3147–3164, arXiv:hep-th/9903050

    Pith/arXiv arXiv 1999

  26. [26]

    Muti-instanton amplitudes in type IIB string theory,

    A. Sen, “Muti-instanton amplitudes in type IIB string theory,”JHEP12(2021) 065,arXiv:2104.15110 [hep-th]

    arXiv 2021

  27. [27]

    D-particle bound states and generalized instantons,

    G. W. Moore, N. Nekrasov, and S. Shatashvili, “D-particle bound states and generalized instantons,” Commun. Math. Phys.209(2000) 77–95, arXiv:hep-th/9803265

    Pith/arXiv arXiv 2000

  28. [28]

    ”Filtering

    H. Liu, “”Filtering” CFTs at large N: Euclidean Wormholes, Closed Universes, and Black Hole Interiors,”arXiv:2512.13807 [hep-th]

    arXiv

  29. [29]

    Wormholes and Averaging over N,

    J. Kudler-Flam and E. Witten, “Wormholes and Averaging over N,”arXiv:2605.15180 [hep-th]

    Pith/arXiv arXiv

  30. [30]

    Einstein gravity from a matrix integral – Part I,

    S. Komatsu, A. Martina, J. a. Penedones, A. Vuignier, and X. Zhao, “Einstein gravity from a matrix integral – Part I,”arXiv:2410.18173 [hep-th]

    arXiv

  31. [31]

    Einstein gravity from a matrix integral – Part II,

    S. Komatsu, A. Martina, J. Penedones, A. Vuignier, and X. Zhao, “Einstein gravity from a matrix integral – Part II,”arXiv:2411.18678 [hep-th]

    arXiv

  32. [32]

    The Polarised IKKT Matrix Model,

    S. A. Hartnoll and J. Liu, “The Polarised IKKT Matrix Model,”arXiv:2409.18706 [hep-th]

    arXiv

  33. [33]

    Supergravity solutions for Dp-D(6−p) bound states: from p = 7 to p =−1,

    S. Reymond, M. Trigiante, and T. Van Riet, “Supergravity solutions for Dp-D(6−p) bound states: from p = 7 to p =−1,”JHEP04(2025) 037, arXiv:2410.02616 [hep-th]

    arXiv 2025

  34. [34]

    Towards an “AdS1/CFT0

    S. E. Aguilar-Gutierrez, K. Parmentier, and T. Van Riet, “Towards an “AdS1/CFT0” correspondence from the D(−1)/D7 system?,”JHEP09 (2022) 249,arXiv:2207.13692 [hep-th]

    arXiv 2022

  35. [35]

    On the D(–1)/D7-brane systems,

    M. Billò, M. Frau, F. Fucito, L. Gallot, A. Lerda, and J. F. Morales, “On the D(–1)/D7-brane systems,”JHEP 04(2021) 096,arXiv:2101.01732 [hep-th]

    arXiv 2021