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arxiv: 2605.25251 · v3 · pith:SYJJLPDKnew · submitted 2026-05-24 · ✦ hep-th · gr-qc

Some universalities in the partition functions of low-dimensional gravity models

Mahdis Ghodrati This is my paper

Pith reviewed 2026-06-29 23:24 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords partition functionsJT gravitylow-dimensional gravityuniversal structuresholographywormholesentanglement entropyChern-Simons theory
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The pith

Partition functions across low-dimensional gravity models display structural universalities.

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

This paper connects various low-dimensional quantum gravity models including 3d Chern-Simons, 2d JT, 2d BF theory, 2d Liouville, 2d WZW, and 1d Schwarzian through holography and dimension reduction. It proposes universalities in their partition functions by comparing the JT partition function to the N=(2,2) partition function on S^2 and AdS2. Parameter changes, eigenfunctions, spectra, Wheeler-DeWitt wavefunctions, entanglement entropy, complexity, RG flows, and wormhole-defect links are used to bolster the case for these universalities. A sympathetic reader would care because such universalities could point to common underlying principles in quantum gravity formulations.

Core claim

The author establishes that similarities between the JT partition function and the N=(2,2) partition function on S^2 and AdS2, along with consistent behaviors under parameter variations and in auxiliary quantities like eigenfunctions and entanglement entropy, indicate the presence of universalities in the partition functions of low-dimensional gravity models.

What carries the argument

The partition functions of the models, particularly their structural responses to parameter changes and the associated wavefunctions and entropy measures.

If this is right

  • Parameter variations will produce analogous changes in partition function structures across the models.
  • Similar spectra and eigenfunctions will appear in the different gravity models.
  • Wheeler-DeWitt wavefunctions will behave similarly in the compared models.
  • Entanglement entropy and complexity will follow universal patterns in wormhole setups.
  • RG flows will exhibit common features linked to the universal partition functions.

Where Pith is reading between the lines

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

  • This suggests that predictions from one model could be transferred to others via the universal structures.
  • Further exploration might connect these to higher-dimensional gravity or string theory models.
  • Numerical checks on entanglement measures could test the universality.
  • The wormhole-defect connections might offer a new way to probe these universalities.

Load-bearing premise

The similarities observed in the partition functions and related quantities arise from fundamental universal features of the models rather than from specific choices in parametrization or coincidental alignments.

What would settle it

Demonstrating that a particular parameter change produces qualitatively different alterations in the JT partition function compared to the N=(2,2) partition function on AdS2 would disprove the universality.

Figures

Figures reproduced from arXiv: 2605.25251 by Mahdis Ghodrati.

Figure 1
Figure 1. Figure 1: The connections between various low-dimensional (2 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The behavior of the spectral form factor in a SYK model, for a sample with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The behavior of the JT integrand is shown for [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The behavior of JT integrand versus s and µ is shown, for the case of n = 1, in the left panel, and n = 2 in the right panel. is shown on the right panel. Most of the partition functions in low-dimensional quantum gravity models could be considered a combination of these two types of functions. On the other hand, the behavior of the integrand of the partition function found in [8] for the case of AdS2 and … view at source ↗
Figure 5
Figure 5. Figure 5: The behavior of the function [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The behavior of AdS2 partition function integrand versus L and σ1 is shown, for the case of L0 = gY M = ρ0 = r = 1. Interestingly, in [22], for the case of a black hole in AdS4, similar to our studies here, rapid fluctuations in the quantity TrE(−1)F as the function of energy E have been detected, where the growth of its envelope has the functional behavior of √ E. This oscillation is mainly due to the 14 … view at source ↗
Figure 7
Figure 7. Figure 7: The behavior of S2 partition function integrand versus L and σ0 for the case of L = ν = ξ = 1. In the left panel, r = 1, and in the right panel, r = 2. -4 -2 2 4 σ0 -0.10 -0.05 0.05 0.10 S2 Partition Function [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The behavior of S2 partition function integrand versus σ0 for the case of L = ν = ξ = 1. The blue curves, whose maxima and minima are constant, correspond to r = 1, the green curves correspond to r = 1.5 and the red curves correspond to r = 1.7. For the case of r > 1, the absolute values of the maxima and minima would increase with increasing σ0. imaginary part of the action, where its frequency is determi… view at source ↗
Figure 9
Figure 9. Figure 9: The behavior of the S 2 partition function in the large r-charge limit. Now we can compare this behavior with other cases. The spacelike spherical partition function 16 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The behavior of the spherical Liouville partition function. [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The behavior of the brane state of the spherical Liouville partition function is shown in the left [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The general behavior of the real part of the wave-function [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The behavior of the real part of the wavefunction [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The behaviors of the wavefunction fs,k(x, y) for even and odd values of b are shown. On the left, b = 6, and on the right, b = 7. The general behavior for other values is similar. Here, s = k = 1. The effects of the quantum number k can also be studied here, where the results are shown in [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The behavior of the wavefunction fs,k(x, y) for different values of k is shown. On the left, k = 2, and on the right, k = 9. Here s = b = 1. For this quantum mechanical system, the canonical partition function is [9] Zparticle = Z ∞ 0 ds Z ∞ 0 dk Z M dxdy y 2 e −β s 2 2 f ∗ s,k(x, y)fs,k(x, y) = VAdS Z ∞ 0 dse−β s 2 2 s 2π sinh(2πs) cosh(2πq) + cosh(2πs) , (2.39) which again has the same structure as we h… view at source ↗
Figure 16
Figure 16. Figure 16: On the left, the exponential part; in the middle, the oscillatory and non-smooth part; and on [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The behavior of the function β(ρ) for the wormhole metric, for b = 3, β1 = 5+i and β2 = 1+2i is shown in the left panel, and the behavior of the function β(ρ) for the wormhole metric, and for the values of b = 3, β1 = 3 + 2i and β2 = 2 + 3i is shown in the right section. 25 [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: The behavior of the function β(ρ) for the wormhole metric, for b = 3, β1 = β2 = 2 is shown in the left panel. If the value of β1 = β2 = n ∈ R, the function β(ρ) is always monotonically decreasing. The behavior of the function H(ρ) for the wormhole metric, for b = 3 is shown in the right section. 1 2 3 4 5 ρ -0.014 -0.012 -0.010 -0.008 -0.006 -0.004 -0.002 β(ρ) 1 2 3 4 5 ρ -0.05 -0.04 -0.03 -0.02 -0.01 β(ρ… view at source ↗
Figure 19
Figure 19. Figure 19: The behavior of the function β(ρ) for the wormhole metric, for b = 3, β1 = 1 + 2i and β2 = 2 + 3i is shown in the left panel and the behavior of the function β(ρ) for the wormhole metric and for b = 3, β1 = β2 = 2i, is shown in the right panel. If we choose the values of β1 = β2 = n, the function β(ρ) is always monotonically increasing. This case has not been considered in [34] though. Therefore, as in th… view at source ↗
Figure 20
Figure 20. Figure 20: The behavior of the function S(ρ) versus L(ρ) for the wormhole metric, for b = 3, β1 = 3 + 2i and β2 = 1 + 2i is shown on the left, the behavior of the function S(ρ) versus L(ρ) for the wormhole metric, for b = 3, β1 = β2 = 4 is shown in the center, and the behavior of the function S(ρ) versus L(ρ) for the wormhole metric, for b = 3, β1 = β2 = 3 on the right parts. As for the precision test, the example o… view at source ↗
Figure 21
Figure 21. Figure 21: The behaviors of level statistics (LS) between two CFTs with different couplings, [PITH_FULL_IMAGE:figures/full_fig_p029_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: The behavior of spectral form factor for [PITH_FULL_IMAGE:figures/full_fig_p030_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: The defect, Γ, is shown in red, and the green line is the null geodesic which has angle ψ with Γ and a distance R from it. spectral form factor (SFF), g(τ ) = DP i,j e −τ(λi−λj ) E , for these two types of deformations was also numerically studied. Here, λi are the eigenvalues of the reduced density matrix. The main universal behaviors were noted in those cases as well. 4 Conclusion In this work, we discu… view at source ↗
read the original abstract

In this work, first, we discuss the connections between various low-dimensional quantum gravity models, including 3d Chern-Simons, 2d JT, 2d BF theory, 2d Liouville, 2d WZW, and 1d Schwarzian, which are related through holography and dimension reduction, and discuss some universalities in their partition functions. Then, we specifically examine the JT partition function and the partition function of $\mathcal{N}=(2,2)$ on $S^2$ and $\text{AdS}_2$ and discuss their similarities and therefore examine our proposed universalities. We change the parameters in each model and based on the change in the structure of the partition functions, strengthen our conjectures. We also use eigenfunctions, spectra and the behaviors of Wheeler-DeWitt wavefunctions to generate more universalities between these low-dimensional quantum gravity models, specifically in their partition functions. Then, we use entanglement entropy, complexity and RG flows, particularly in the context of wormholes, to find more universalities in quantum gravity models. Finally, we use the new results about the connections between wormholes and defects to discuss our universalities further.

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

3 major / 1 minor

Summary. The manuscript claims that universalities exist in the partition functions of low-dimensional quantum gravity models (3d Chern-Simons, 2d JT, 2d BF, 2d Liouville, 2d WZW, 1d Schwarzian) related by holography and dimensional reduction. It focuses on structural similarities between the JT partition function and the N=(2,2) partition function on S^2 and AdS2, conjecturing these universalities are strengthened by parameter variations and further supported by eigenfunctions, spectra, Wheeler-DeWitt wavefunctions, entanglement entropy, complexity, RG flows, and wormhole-defect connections.

Significance. If the conjectures hold and can be made precise, they would indicate common structural features in partition functions across these models that extend beyond their established holographic and reduction relations, potentially unifying aspects of low-dimensional quantum gravity. The breadth of auxiliary quantities examined (entanglement entropy, complexity, RG flows) provides multiple angles for exploration. However, the absence of quantitative metrics, derivations, or falsifiable predictions means the work primarily flags patterns rather than establishing robust results, limiting its immediate significance to suggesting directions for follow-up research.

major comments (3)
  1. [Abstract] Abstract: The central claims are presented as conjectures strengthened by parameter variation and qualitative similarities, but no derivations, error estimates, or falsifiable predictions are supplied, leaving the evidential support for the universalities weak.
  2. [Abstract] Abstract: The approach of changing parameters in each model and using resulting changes in partition function structure to strengthen the conjectures risks circularity, as the universalities may be defined in terms of the similarities being invoked to support them.
  3. [Abstract] Abstract: The models are explicitly connected through holography and dimension reduction; a precise, model-independent definition of 'universality' is required to determine whether the observed partition function similarities reflect new structure or are expected consequences of these known relations.
minor comments (1)
  1. [Abstract] The abstract is lengthy and lists many auxiliary quantities without clear prioritization; separating the core partition function claims from the supporting observables would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive criticism of our manuscript. We address each major comment in turn below, providing clarifications on the scope of our conjectures and indicating revisions where appropriate to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claims are presented as conjectures strengthened by parameter variation and qualitative similarities, but no derivations, error estimates, or falsifiable predictions are supplied, leaving the evidential support for the universalities weak.

    Authors: We agree that the manuscript is exploratory in nature and presents conjectures based on observed structural patterns rather than rigorous derivations or quantitative metrics. The support comes from qualitative similarities in partition functions across models, their persistence under parameter changes, and connections to auxiliary quantities such as wavefunctions and entanglement. No error estimates or falsifiable predictions are provided because the work aims to flag potential universal features for future investigation. We will revise the abstract to more explicitly characterize the claims as conjectures and to note the qualitative character of the evidence. revision: partial

  2. Referee: [Abstract] Abstract: The approach of changing parameters in each model and using resulting changes in partition function structure to strengthen the conjectures risks circularity, as the universalities may be defined in terms of the similarities being invoked to support them.

    Authors: We maintain that the argument is not circular. The conjectured universalities are motivated by the established holographic and dimensional-reduction relations among the models. Parameter variations are then employed to examine whether the partition-function similarities remain robust under deformations, which would indicate they are intrinsic features rather than artifacts of particular parameter choices. This is a standard approach for identifying universal behavior. We will add a clarifying sentence in the revised abstract to distinguish the initial motivation from the robustness test. revision: no

  3. Referee: [Abstract] Abstract: The models are explicitly connected through holography and dimension reduction; a precise, model-independent definition of 'universality' is required to determine whether the observed partition function similarities reflect new structure or are expected consequences of these known relations.

    Authors: We accept that a precise definition would improve clarity. In the revised manuscript we will supply a working definition: universality here refers to structural features of the partition functions (e.g., specific functional forms or parameter dependences) that appear across the models in ways not directly implied by the known holographic or reduction mappings. We will illustrate how the JT–N=(2,2) similarities, together with the auxiliary quantities examined, point to additional common structure beyond those mappings. revision: yes

Circularity Check

2 steps flagged

Universalities conjectured from observed partition-function similarities after parameter variation, with models already linked by holography/reduction

specific steps
  1. self definitional [Abstract]
    "We change the parameters in each model and based on the change in the structure of the partition functions, strengthen our conjectures. We also use eigenfunctions, spectra and the behaviors of Wheeler-DeWitt wavefunctions to generate more universalities between these low-dimensional quantum gravity models, specifically in their partition functions."

    The universalities are strengthened and generated directly from the observed changes in partition-function structure and auxiliary quantities upon parameter variation; thus the claimed universalities are equivalent to the similarities being used to support them, with no external benchmark or independent derivation.

  2. renaming known result [Abstract]
    "first, we discuss the connections between various low-dimensional quantum gravity models, including 3d Chern-Simons, 2d JT, 2d BF theory, 2d Liouville, 2d WZW, and 1d Schwarzian, which are related through holography and dimension reduction, and discuss some universalities in their partition functions. Then, we specifically examine the JT partition function and the partition function of N=(2,2) on S^2 and AdS2 and discuss their similarities and therefore examine our proposed universalities."

    The models are already connected by holography and dimension reduction (explicitly listed), so shared partition-function features are expected; presenting these as 'universalities' renames the known relations without supplying a new, falsifiable criterion independent of the connections.

full rationale

The paper's central claim of universalities rests on structural similarities in partition functions (JT vs N=(2,2) on S^2/AdS2) that are examined after explicit parameter changes, plus auxiliary quantities like spectra and wavefunctions. These similarities are invoked to 'strengthen our conjectures' and 'generate more universalities,' but the models are stated to be connected by construction via holography and dimension reduction. No independent, model-independent definition or quantitative measure of universality is supplied that would survive reparametrization or apply outside the known relations, so the claimed universalities reduce to a renaming of expected shared features rather than an independent derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the assumption that the listed models are related through holography and dimension reduction, plus the interpretive step that parameter-induced similarities indicate universality. No free parameters are explicitly fitted in the abstract, but the approach of varying parameters to 'strengthen conjectures' implies ad-hoc choices. No new entities are introduced.

axioms (1)
  • domain assumption The models (3d Chern-Simons, 2d JT, 2d BF, 2d Liouville, 2d WZW, 1d Schwarzian) are related through holography and dimension reduction
    Invoked in the first sentence of the abstract as the basis for discussing universalities.

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