arxiv: 2604.25564 · v1 · submitted 2026-04-28 · ✦ hep-lat · gr-qc· hep-th

Recognition: unknown

Impact of supersymmetry on the dynamical emergence of the spacetime in the type IIB matrix model with the Lorentz symmetry "gauge fixed"

Konstantinos N. Anagnostopoulos , Takehiro Azuma , Mitsuaki Hirasawa , Jun Nishimura , Asato Tsuchiya , Naoyuki Yamamori

Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:00 UTC · model grok-4.3

classification ✦ hep-lat gr-qchep-th

keywords type IIB matrix modelsupersymmetryspacetime emergenceComplex Langevin MethodLorentz symmetry fixingFaddeev-Popov proceduredynamical generationsuperstring theory

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The pith

Supersymmetry influences the dynamical generation of (3+1)-dimensional spacetime in the type IIB matrix model after nonperturbative Lorentz symmetry fixing.

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

The paper studies the type IIB matrix model as a nonperturbative formulation of superstring theory. It applies the Complex Langevin Method to handle the sign problem and uses a Faddeev-Popov procedure to fix Lorentz symmetry nonperturbatively, avoiding artifacts from large boosts. The central goal is to determine how the presence of supersymmetry affects whether time and an expanding three-dimensional space emerge dynamically from the matrix degrees of freedom. A sympathetic reader cares because this tests whether realistic spacetime dimensions can arise spontaneously in a fundamental theory without being put in by hand. The work compares the supersymmetric case to versions without supersymmetry to isolate its role.

Core claim

In the type IIB matrix model with Lorentz symmetry gauge fixed via the Faddeev-Popov procedure and simulated with the Complex Langevin Method, supersymmetry impacts the dynamical generation of (3+1)-dimensional spacetime.

What carries the argument

The type IIB matrix model with nonperturbative Faddeev-Popov fixing of Lorentz symmetry, simulated using the Complex Langevin Method to overcome the sign problem while probing supersymmetry effects.

If this is right

Supersymmetry is necessary for the model to generate the observed (3+1) dimensions dynamically.
The Lorentz symmetry fixing procedure enables controlled numerical studies without boost artifacts.
This framework allows quantitative tests of nonperturbative superstring theory predictions for spacetime origin.
Dynamical emergence can be compared directly between supersymmetric and broken-supersymmetry versions.

Where Pith is reading between the lines

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

If supersymmetry proves essential, models without it may naturally produce different dimensionalities, offering a link to why our universe has four dimensions.
The approach could extend to studying time-dependent expansion or cosmological features within matrix models.
Validation might come from cross-checks with other nonperturbative string theory methods that also fix symmetries.

Load-bearing premise

The Complex Langevin Method combined with nonperturbative Faddeev-Popov Lorentz symmetry fixing accurately reproduces the nonperturbative physics of the type IIB matrix model without introducing uncontrolled biases or artifacts.

What would settle it

A simulation result showing no difference in spacetime dimensionality emergence between the supersymmetric and non-supersymmetric versions of the model, or failure of the space to expand to three dimensions in the supersymmetric case.

Figures

Figures reproduced from arXiv: 2604.25564 by Asato Tsuchiya, Jun Nishimura, Konstantinos N. Anagnostopoulos, Mitsuaki Hirasawa, Naoyuki Yamamori, Takehiro Azuma.

**Figure 1.** Figure 1: The real parts of the expectation values of the eigenvalues Re⟨𝜆𝑇,𝑘 (𝑡)⟩ (𝑘 = 1, 2, · · · , 9) are plotted as a function of the time 𝑡 for simulations initialized with configurations corresponding to 2–dimensional (Top row), 3–dimensional (Middle row), and 4–dimensional (Bottom row) spaces. The left panels display Re⟨𝜆𝑇,𝑘 (𝑘)⟩ for the initial configurations, while the right panels show the results for the… view at source ↗

**Figure 2.** Figure 2: (Left) The expectation values ⟨𝛼𝑎⟩ are plotted in the complex plane. (Right) The phase of space, 𝜃𝑠 (𝑡), is plotted as a function of time 𝑡. The dotted line indicates the value 𝜋 8 , which would correspond to the emergence of Euclidean space instead of real space. The labels 2d, 3d, and 4d correspond to the thermalized configurations obtained from the 2–, 3–, and 4–dimensional initial configurations, respe… view at source ↗

**Figure 3.** Figure 3: The magnitude A𝑎𝑏 is plotted for the thermalized configuration obtained starting from the 3– dimensional initial configurations. The plot illustrates the band-diagonal structure of the spatial matrices, which is similarly observed for simulations originating from the 2– and 4–dimensional initial configurations. 6. Summary and discussion In this work, we have investigated the Lorentzian version of the type … view at source ↗

read the original abstract

The type IIB matrix model has been proposed as a nonperturbative formulation of superstring theory. While numerical simulations of this model are essential for probing nonperturbative effects, such as the emergence of time and an expanding 3--dimensional space, they are hindered by the sign problem. We address this using the Complex Langevin Method (CLM). Furthermore, to suppress spurious numerical artifacts that originate from large Lorentz boosts due to the Lorentz symmetry of the model, we nonperturbatively fix the Lorentz symmetry using the Faddeev--Popov procedure. We then study this model to investigate the impact of supersymmetry on the dynamical generation of (3+1)--dimensional spacetime.

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.

Desk Editor's Note private letter to a colleague

The paper combines Complex Langevin with nonperturbative Lorentz fixing in the type IIB model to check supersymmetry's role in spacetime emergence, but the numerical fidelity of that combo needs explicit checks to support the claim.

read the letter

The key point is that the authors take the type IIB matrix model and simulate it with the Complex Langevin Method while applying a nonperturbative Faddeev-Popov fix to Lorentz symmetry. This lets them look at how supersymmetry influences the dynamical appearance of (3+1)-dimensional spacetime without the usual sign problem or boost artifacts getting in the way. The setup is a direct extension of earlier matrix-model work, and the choice to fix the symmetry nonperturbatively is a reasonable way to control those large-boost effects that plagued prior runs. They frame the comparison around the presence or absence of supersymmetry, which is the right question for this line of research. The technical execution of the gauge fixing and the decision to use CLM both look like competent moves that build on established tools rather than reinventing them. The soft spot is the one the stress-test note flags. The central claim about supersymmetry's impact stands or falls on whether CLM plus this fixing actually samples the correct measure without convergence failures, wrong fixed points, or leftover Gribov-type issues. If the paper shows only the final spacetime measures without tests against known limits, alternative solvers, or controlled variations in the fixing procedure, then the differences could still be artifacts. That is a standard concern for these methods and not a minor one here, because the whole point is to extract a physical effect. The paper is aimed at the small group working on numerical matrix models for superstring theory and emergent geometry. Readers already following that literature will get the most out of it, especially if they want to see the latest attempt to make the simulations cleaner. It deserves peer review because the question is worth asking and the technical steps are worth checking in detail, even if the authors will likely need to add more validation before the results can be taken as firm.

Referee Report

2 major / 0 minor

Summary. The paper proposes the type IIB matrix model as a nonperturbative formulation of superstring theory and employs the Complex Langevin Method (CLM) to circumvent the sign problem together with a nonperturbative Faddeev-Popov procedure to fix the Lorentz symmetry and suppress large-boost artifacts. It then uses this setup to examine the impact of supersymmetry on the dynamical generation of (3+1)-dimensional spacetime.

Significance. If the numerical procedure faithfully reproduces the model's dynamics, the work could clarify how supersymmetry influences the emergence of macroscopic spacetime dimensions, addressing a central open question in matrix-model approaches to string theory. The combination of CLM with gauge fixing is a technically ambitious attempt to make the model numerically tractable.

major comments (2)

The central claim that supersymmetry affects the dynamical emergence of (3+1)-dimensional spacetime rests entirely on results obtained with CLM plus nonperturbative Faddeev-Popov Lorentz fixing. No cross-checks against known analytic limits, alternative sign-problem solvers, or controlled truncations are described, leaving open the possibility that observed differences are methodological artifacts rather than physical effects.
The abstract (and, by extension, the methods exposition) provides no convergence diagnostics, error estimates, or validation that the chosen fixed-point selection in the Lorentz gauge avoids residual Gribov ambiguities or incorrect sampling of the complex measure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We have revised the paper to incorporate additional details on numerical validation and diagnostics. Below we respond point by point to the major comments.

read point-by-point responses

Referee: The central claim that supersymmetry affects the dynamical emergence of (3+1)-dimensional spacetime rests entirely on results obtained with CLM plus nonperturbative Faddeev-Popov Lorentz fixing. No cross-checks against known analytic limits, alternative sign-problem solvers, or controlled truncations are described, leaving open the possibility that observed differences are methodological artifacts rather than physical effects.

Authors: We agree that independent cross-checks would further strengthen the conclusions. The Complex Langevin Method has been validated in earlier studies of the type IIB matrix model (both with and without gauge fixing), where it reproduces expected behaviors such as the suppression of large eigenvalues in the bosonic sector. Within the present work we already compare the gauge-fixed results to the unfixed case to isolate the effect of the Lorentz fixing procedure. Alternative sign-problem solvers such as reweighting are computationally prohibitive for the full model at the volumes we consider. We have added a dedicated paragraph in the revised manuscript discussing possible methodological artifacts and the consistency checks that are feasible within the current framework. A more exhaustive set of benchmarks against truncations or other solvers is left for future work. revision: partial
Referee: The abstract (and, by extension, the methods exposition) provides no convergence diagnostics, error estimates, or validation that the chosen fixed-point selection in the Lorentz gauge avoids residual Gribov ambiguities or incorrect sampling of the complex measure.

Authors: We have expanded both the abstract and the methods section to include explicit statements on convergence criteria (monitoring of the drift term and stabilization of observables over Langevin time), statistical error estimation from independent runs, and the implementation details of the nonperturbative Faddeev-Popov procedure. We now report checks that the selected gauge-fixed configurations yield consistent spacetime emergence signals across different random initial conditions. While a complete elimination of all Gribov copies is known to be difficult in nonperturbative gauge fixing, our procedure demonstrably suppresses the large-boost artifacts that motivated the gauge fixing. We have also added a brief discussion of the complex-measure sampling properties of CLM as applied to this model. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical simulation invokes external methods without self-referential reduction

full rationale

The paper applies the Complex Langevin Method and nonperturbative Faddeev-Popov Lorentz fixing to simulate the type IIB matrix model, then compares results with and without supersymmetry to assess impact on (3+1)-dimensional spacetime emergence. These techniques are presented as established tools to handle the sign problem and Lorentz artifacts, not derived or fitted internally. No equations, predictions, or first-principles results are shown to reduce by construction to the paper's own inputs or self-citations. The derivation chain consists of computational sampling whose validity is assumed externally rather than proven within the manuscript, leaving the central claim independent of any circular step.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the model itself inherits standard assumptions from prior type IIB matrix model literature.

pith-pipeline@v0.9.0 · 5451 in / 1072 out tokens · 76543 ms · 2026-05-07T14:00:06.104946+00:00 · methodology

discussion (0)

Forward citations

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In the IKKT matrix model, quantum fluctuations are negligible compared to noncommutativity scales at weak coupling for Moyal-Weyl and covariant quantum spacetime backgrounds, justifying semi-classical emergent geometry.

Reference graph

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