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REVIEW 3 major objections 5 minor 83 references

Absorbing the large-R holonomy term −A into a shifted Gaussian recovers the universal −2d continuum free-energy law via Wishart saddles.

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2026-07-10 06:46 UTC pith:Y3WAGYB5

load-bearing objection Solid technical step that recovers the continuum -2d DΛ-channel via Wishart/Stiefel variables and a pure -A benchmark; the balanced +A split is the real soft spot but does not sink the paper. the 3 major comments →

arxiv 2607.08481 v1 pith:Y3WAGYB5 submitted 2026-07-09 hep-th gr-qchep-lathep-phmath-phmath.MP

Gram--Wishart--Stiefel formulation of the N=2, large--d gauge theory in 1D

Badis Ydri This is my paper
classification hep-th gr-qchep-lathep-phmath-phmath.MP
keywords BFSS matrix modelBMN matrix modelWishart variablesStiefel manifoldsholonomy dynamicslarge-d expansionBessel kernelplanar endpoint theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper rewrites the N=2 large-d planar endpoint theory of BFSS/BMN matrix quantum mechanics on the lattice in Gram/Wishart/Stiefel variables: endpoint vectors become rank-two Wishart eigenvalues plus relative Stiefel angles. The dominant large-R aligned piece of the holonomy potential is the linear term −A; absorbing it into the Gaussian sector produces the shifted mass (α_Λ)_eff = α_Λ − 1/2, which the exact O(2) integral encodes as a rank-two Bessel kernel. Finite polynomial truncations of the remaining transverse B-potential create an artificial large-d perturbativity bound incompatible with the continuum, but summing the local completion and balancing the compensating +A term restores the physical Wishart saddle. The continuum free-energy ratio then behaves as log(Z_W(x)/Z_W(0)) = −2(d−2)x^{2} + O(x^{4}), reproducing the universal D_Λ-channel contribution. A sympathetic reader cares because this isolates how holonomy dynamics and continuum scaling already sit inside the radial Wishart measure and angular kernel of matrix quantum mechanics, without needing the full anisotropic β_Λ channel.

Core claim

After the large-R linear contribution −A is absorbed into the Gaussian sector (producing the shifted mass (α_Λ)_eff = α_Λ − 1/2) and the residual transverse potential is replaced by its summed non-polynomial completion with a balanced compensating +A split, the Wishart saddle is recovered with the physical shifted mass; the continuum free-energy ratio then satisfies log(Z_W(x)/Z_W(0)) = −2(d−2)x^{2} + O(x^{4}), reproducing the universal −2d D_Λ-channel of the exact endpoint theory.

What carries the argument

The rank-two orthogonal Bessel/HCIZ angular kernel obtained from the exact O(2) integral over relative Stiefel and planar angles; its exponential selects the aligned configuration while its prefactor cancels the spurious doubled Wishart entropy, fixing the pure −A theory and enabling the shifted Wishart analysis of the transverse sector.

Load-bearing premise

The compensating +A term must be split by a large non-convex weight so that residual linear slopes cancel at a flat point; without a consistent such split the continuum mass is corrupted and the universal −2d law fails.

What would settle it

Evaluate the continuum free-energy ratio for the completed transverse potential with the compensating +A term left unsplit (or with weight w = 1) and check whether it still yields −2(d−2)x^{2} or instead produces a renormalized mass that spoils the universal coefficient.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Pure transverse B-type models capture only the universal D_Λ-channel −2d contribution; the anisotropic β_Λ-channel requires the longitudinal invariant A to remain dynamical.
  • Apparent large-d perturbativity bounds arising from finite polynomial truncations are truncation artifacts and disappear once the full non-polynomial completion is restored.
  • The endpoint Wishart measure already encodes the −2d coefficient via the shifted Gaussian normalization, before any residual holonomy interaction is added.
  • Continuum fine-tuning of the shifted mass is controlled by large-R holonomy asymptotics rather than by the bare Gaussian data alone.

Where Pith is reading between the lines

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

  • The same Bessel/HCIZ factorization may allow reduced Wishart Monte-Carlo sampling of continuum free energies in higher-N or higher-d regimes without sampling the full matrix coordinates.
  • A variational principle that systematically cancels residual linear slopes after completion could replace the numerical balanced split in related endpoint formulations.
  • Hybrid A-B formulations that keep the longitudinal mode dynamical are required if one wishes to recover the full d(d+1) anisotropic channel alongside the universal −2d piece.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reformulates the N=2, large-d planar endpoint theory of lattice BFSS/BMN matrix quantum mechanics in Gram/Wishart/Stiefel variables: rank-two Wishart eigenvalues and relative Stiefel angles. The large-R aligned holonomy asymptotics contribute a universal linear term −A, which is absorbed into the Gaussian sector to produce the shifted mass (α_Λ)_eff = α_Λ − 1/2. The exact O(2) integral yields a rank-two Bessel kernel; the pure −A theory, solved exactly in Cartesian variables, fixes the leading Bessel/HCIZ structure (aligned exponential plus a prefactor that cancels the spurious doubled Wishart entropy). Applied to the transverse B-type expansion and a non-polynomial toy completion V_toy = −log cosh B, finite polynomial truncations produce an apparent large-d perturbativity bound incompatible with the continuum; after a summed local completion and a balanced compensating split of the +A term, the Wishart saddle is recovered with the physical shifted mass and the continuum free-energy ratio log(Z_W(x)/Z_W(0)) = −2(d−2)x² + O(x⁴), reproducing the universal D_Λ-channel −2d contribution. The anisotropic β_Λ-channel is stated to lie outside pure transverse B-type descriptions.

Significance. If the construction holds, it supplies a systematic radial/angular dictionary for the planar endpoint theory and isolates how the universal D_Λ-channel −2d is already encoded in the shifted Wishart measure after Bessel resummation of −A. The pure −A Cartesian identity (6.32)–(6.33) is an independent, parameter-free benchmark that cleanly fixes the leading kernel prefactor and cancels doubled Wishart entropy; that step is a genuine technical contribution. The continuum coefficient is not fitted but follows from the shifted mass M = α_Λ − 1/2. The work is part of a multi-paper program and is most valuable as a structural reformulation rather than a new physical prediction; its significance for matrix quantum mechanics and large-d holonomy dynamics is real but incremental, and depends on controlling the residual approximations (weak-minor truncation, toy completion, and the balanced +A split).

major comments (3)
  1. §8.2.1, Eqs. (8.47)–(8.50): the recovery of the physical mass M = α_Λ − 1/2 (and hence the claimed continuum law (8.60)) rests on a balanced compensating split +A = (1−w)A + wA with w fixed numerically so that the residual linear slope vanishes at a new flat point. For R_* ≃ 1.545 and A_d ≃ 1/2 the paper reports w ≃ 3.75 (a large add–subtract, not a convex partition). No existence/uniqueness argument is given for general R_* or under continuum scaling of R_*, and the text itself notes that without the split one obtains M_flat = M + (1/2)K_flat, which would alter the continuum expansion. This is load-bearing for the abstract’s claim that the Wishart saddle is recovered with the physical shifted mass. Either a general existence proof (or continuum-controlled construction) of the split, or a clear statement that the −2d law is conditional on this bookkeeping device and fails if the residual
  2. §§4.4–5.2 and 7.1: the continuum analysis is carried out under the weak-minor (or improved weak-minor) truncation δ → 0, with the residual κ-dependent determinant splitting suppressed while ρ_± still retain two-branch memory. The paper does not quantify the error of this truncation on the continuum free-energy coefficient, nor show that the omitted minor sector cannot renormalize M or generate O(d) corrections that compete with −2(d−2)x². Since the pure −A sector is treated nonperturbatively but the transverse sector is not, a controlled estimate (or an explicit argument that the minor contribution is subleading in the continuum scaling of R) is needed before the D_Λ-channel claim can be regarded as established within the Gram formulation.
  3. §6.3.3, Eq. (6.45) and §7.1, Eq. (7.8): the rank-two orthogonal Bessel/HCIZ kernel is introduced as a structural ansatz whose exponential is fixed by large-argument alignment and whose prefactor is fixed by the Cartesian identity (6.33). The residual factor P(v,w;ℓ) is asserted to be subleading for continuum scaling, but no bound or asymptotic control on P is given. Because the cancellation of one full Wishart entropy block is essential to obtaining a single soft Gaussian block (and thus −2d rather than ∼−4d), the continuum coefficient inherits any uncontrolled contribution from P. A sharper statement of what is proven versus assumed for K_d would strengthen the central pure −A result.
minor comments (5)
  1. Figure 2 is referenced as contrasting the toy and quartic B-potentials but is not described in enough detail in the caption for a reader who cannot see the plot; a short quantitative caption (e.g., location of artificial minima of the quartic) would help.
  2. Notation for the shifted mass is not fully uniform: (α_Λ)_eff, M, and meff appear in different sections for closely related quantities; a single convention table early in §1.3 would reduce friction.
  3. The manuscript relies extensively on the author’s prior endpoint and large-d papers [76–81]. For a standalone reading, a short self-contained recap of the constrained saddle R_* ≃ 1.545 and of the exact continuum split C_ex_2 → d(d−1) would help non-specialists.
  4. §3.1: the Bernoulli asymptotics of c_{2n} are given, but the radius of convergence of the toy series in the physical B-range is not stated; one sentence would clarify that the series is only a local diagnostic.
  5. Typos and style: “eVhol” / “eVtoy” notation for completed potentials is easy to misread in plain text; consider a more distinctive accent or a roman “comp” subscript consistently. Occasional long sentences in §§1.3 and 8.1 could be split for readability.

Circularity Check

2 steps flagged

Balanced +A split recovers the known -2d Wishart law by construction of the vanishing-slope condition; target D-channel and endpoint setup load-bearing on author's prior series.

specific steps
  1. self definitional [Sec. 8.2.1–8.2.2, Eqs. (8.47)–(8.50) and (8.60)]
    "The parameter w is fixed by requiring the residual linear slope to vanish at the new flat point. ... Once this balanced split is imposed, the completed transverse sector no longer renormalizes the continuum mass. The effective leading problem therefore reduces cleanly to the Wishart form with the original shifted mass M=α_Λ-1/2 ... log Z_W(x)/Z_W(0)=-2(d-2)x^{2}+O(x^{4})."

    w is defined by the two conditions that set K_tot_w=0 (and the flat-point relation). By that definition the residual linear term vanishes, the free energy is forced to be exactly that of the pure shifted Wishart FW(u)=2Mu-(d-2)log u, and the continuum expansion of M(x) then automatically produces -2(d-2)x^{2}. The 'recovery' of the physical mass and of the universal -2d law is therefore true by construction of the split, not an independent dynamical result.

  2. self citation load bearing [Abstract; Sec. 1.3.1; Sec. 2; references [76–81,79]]
    "We develop in this paper the Gram/Wishart/Stiefel formulation of the N=2, large-d planar endpoint theory of the BFSS/BMN matrix quantum mechanics on the lattice, obtained in our previous work. ... In the exact theory ... C_ex_2,D o-2d ... This is the key motivation for Section 3."

    The entire planar boundary model, the constrained saddle R_*≃1.545, the holonomy potential, the continuum fine-tuning of α_Λ and β_Λ, and the target universal D_Λ-channel coefficient -2d are imported from the author's own preceding papers in the series. Those results are not re-derived from first principles here (except for the pure -A special case) and are load-bearing for both the setup and the claim that the completed theory 'reproduces' the known continuum law.

full rationale

The pure -A theory is solved independently via Cartesian Gaussian integrals (Sec. 6.2) and supplies a genuine external benchmark that fixes the Bessel/HCIZ kernel ansatz and already yields the -2d coefficient without any split. The toy model is an explicit ansatz whose Gaussian average is computed exactly and designed to match the known D_Λ singularity. These steps are not circular. However, the strongest continuum claim for the completed transverse theory (recovery of the physical shifted mass and log(Z_W(x)/Z_W(0)) = -2(d-2)x^{2}) is obtained only after a balanced compensating split whose parameter w is defined by the simultaneous numerical conditions that force the residual linear slope to vanish. Once that definition is imposed, the free energy reduces by construction to the pure shifted Wishart whose continuum expansion is already known. In addition the planar endpoint model, R_*, holonomy potential, and the target D-channel continuum structure are taken from the author's prior works [76–81,79] and are load-bearing for the setup. The circularity is therefore real but partial and localized; the independent pure -A calculation keeps the overall score moderate.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 2 invented entities

The central continuum claim rests on the large-d Gaussian reduction and endpoint formulation already derived in the author’s prior works, on the standard Wishart/Stiefel measure, on the large-R asymptotic of the holonomy potential, and on two paper-specific constructions (the non-polynomial toy completion and the balanced +A split). No free parameters are fitted to external data; the numerical values R_* and w are determined by transcendental equations internal to the model.

axioms (6)
  • domain assumption Large-d Gaussian reduction of BFSS/BMN yields a self-consistent gauged matrix harmonic oscillator whose singlet sector is a Molien–Weyl integral (prior works [76–81]).
    Invoked throughout §§1–2 as the starting point of the planar endpoint theory.
  • domain assumption After bulk integration the N=2 theory reduces to two sets of d transverse 2-vectors whose holonomy invariants are A, B, R with potential V_hol = -log(I_0(R) - (A/R)I_1(R)).
    Taken from the author’s previous endpoint paper [79] and used as the definition of the planar boundary model (§2).
  • standard math The large-R aligned asymptotics of the boundary potential is V_b(R) ∼ -R + O(log R), so the linear -A may be absorbed into the Gaussian sector.
    Standard modified-Bessel asymptotics (2.31)–(2.34); the absorption step itself is a modeling choice of the paper.
  • standard math Rank-two Wishart/Stiefel Jacobian for 2 imes d matrices: measure ∝ (v1 v2)^{(d-3)/2}|v1-v2| dv1 dv2 dµ(R_V) dµ(U0) (and likewise for W).
    Classical multivariate-statistics fact (Wishart, James, Herz) used in §4.2.
  • ad hoc to paper The non-polynomial toy potential V_toy(B) = -log cosh B captures the singular D_Λ-channel of the exact holonomy kernel after Gaussian averaging.
    Introduced in §3 as a representative completion; justified by matching the continuum singularity but not derived from the exact holonomy potential.
  • ad hoc to paper A balanced compensating split +A = (1-w)A + wA with w chosen so residual linear slope vanishes exists and preserves the physical mass shift.
    Constructed numerically in §8.2.1; no general existence proof is given.
invented entities (2)
  • Rank-two orthogonal Bessel/HCIZ angular kernel K_d(v,w;ℓ) no independent evidence
    purpose: Encodes the exact O(2) integral of the shifted -A source and supplies the inverse-Wishart prefactor that cancels doubled entropy.
    Defined by the pure -A Cartesian identity (6.33) and the structural ansatz (6.45); its leading exponential and prefactor are fixed by that identity, but the residual factor P remains unspecified.
  • Balanced compensating split weight w of the +A term no independent evidence
    purpose: Cancels the residual linear slope of the completed transverse potential so that the continuum mass remains M = α_Λ - 1/2.
    Introduced ad hoc in §8.2.1; numerical value w ≈ 3.75 is chosen to satisfy the flat-point and vanishing-slope conditions for the specific R_* of the model.

pith-pipeline@v1.1.0-grok45 · 61243 in / 3827 out tokens · 35786 ms · 2026-07-10T06:46:19.435761+00:00 · methodology

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read the original abstract

We develop in this paper the Gram/Wishart/Stiefel formulation of the \(N=2\), large--\(d\) planar endpoint theory of the BFSS/BMN matrix quantum mechanics on the lattice, obtained in our previous work. In this formulation, the endpoint degrees of freedom are reorganized into rank--two Wishart eigenvalues and relative Stiefel angular variables. This allows the holonomy invariants \(A\), \(B\), and \(R^2=A^2+B^2\) to be analyzed directly in terms of radial and angular Gram data. A central point is the large-\(R\) aligned asymptotics of the holonomy potential. Its universal linear contribution \(-A\) is absorbed into the Gaussian sector, producing the shifted mass parameter \((\alpha_\Lambda)_{\rm eff}=\alpha_\Lambda-1/2\). In the Gram/Wishart/Stiefel variables, the exact \(O(2)\) angular integral encodes this shifted sector in a rank--two Bessel kernel. The pure \(-A\) theory, which is exactly solvable in Cartesian variables, then fixes the leading Bessel/HCIZ structure: its exponential part selects the aligned configuration, while its prefactor removes the spurious doubled Wishart entropy. We then apply this structure to the transverse \(B\)-type expansion and its non-polynomial toy completion. Finite polynomial truncations lead to an apparent large--\(d\) perturbativity bound incompatible with the continuum limit, but this bound is shown to be an artifact of truncation. After summing the local transverse completion and balancing the compensating \(+A\) term, the Wishart saddle is recovered with the physical shifted mass. The resulting continuum behavior reproduces the universal \(-2d\) contribution of the \(D_\Lambda\)-channel, while the genuinely anisotropic \(\beta_\Lambda\)-channel lies outside the scope of a pure transverse \(B\)-type description.

Figures

Figures reproduced from arXiv: 2607.08481 by Badis Ydri.

Figure 1
Figure 1. Figure 1: The static diagonal (Polyakov) gauge. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The toy versus the quadratic B-potential. [PITH_FULL_IMAGE:figures/full_fig_p038_2.png] view at source ↗

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Works this paper leans on

83 extracted references · 83 canonical work pages · 33 internal anchors

  1. [1]

    Supersymmetric Yang-Mills Theories,

    L. Brink, J. H. Schwarz and J. Scherk, “Supersymmetric Yang-Mills Theories,” Nucl. Phys. B121, 77-92 (1977)

    work page 1977

  2. [2]

    Fierz Identities for Real Clifford Algebras and the Number of Supercharges,

    M. Baake, M. Reinicke and V. Rittenberg, “Fierz Identities for Real Clifford Algebras and the Number of Supercharges,” J. Math. Phys.26, 1070 (1985)

    work page 1985

  3. [3]

    ’t Hooft,A Planar Diagram Theory for Strong Interactions, Nucl

    G. ’t Hooft,A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B72, 461 (1974)

    work page 1974

  4. [4]

    Dimensional Reduction in Quantum Gravity

    G. ’t Hooft,Dimensional Reduction in Quantum Gravity, arXiv:gr-qc/9310026

    work page internal anchor Pith review Pith/arXiv arXiv

  5. [5]

    Susskind,The World as a Hologram, J

    L. Susskind,The World as a Hologram, J. Math. Phys.36, 6377 (1995)

    work page 1995

  6. [6]

    M Theory As A Matrix Model: A Conjecture

    T. Banks, W. Fischler, S. H. Shenker and L. Susskind, “M theory as a matrix model: A conjecture,” Phys. Rev. D55, 5112-5128 (1997) [arXiv:hep-th/9610043 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  7. [7]

    Witten,Bound States of Strings andp-Branes, Nucl

    E. Witten,Bound States of Strings andp-Branes, Nucl. Phys. B460, 335 (1996)

    work page 1996

  8. [8]

    Itzhaki, J

    N. Itzhaki, J. M. Maldacena, J. Sonnenschein and S. Yankielowicz,Supergravity and the LargeNLimit of Theories with Sixteen Supercharges, Phys. Rev. D58, 046004 (1998). 93

    work page 1998

  9. [9]

    Polchinski,Dirichlet Branes and Ramond–Ramond Charges, Phys

    J. Polchinski,Dirichlet Branes and Ramond–Ramond Charges, Phys. Rev. Lett.75, 4724 (1995)

    work page 1995

  10. [10]

    Cremmer, B

    E. Cremmer, B. Julia, and J. Scherk,Supergravity Theory in Eleven Dimensions, Phys. Lett. B76, 409 (1978)

    work page 1978

  11. [11]

    String theory dynamics in various dimensions,

    E. Witten, “String theory dynamics in various dimensions,”Nucl. Phys. B443, 85 (1995)

    work page 1995

  12. [12]

    Quantum M-wave and Black 0-brane

    Y. Hyakutake, “Quantum M-wave and Black 0-brane,” JHEP09, 075 (2014) [arXiv:1407.6023 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  13. [13]

    Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry

    Y. Hyakutake and S. Ogushi, “Higher derivative corrections to eleven dimensional super- gravity via local supersymmetry,” JHEP02, 068 (2006) [arXiv:hep-th/0601092 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  14. [14]

    Hoppe,Quantum Theory of a Massless Relativistic Surface and a Two-Dimensional Bound State Problem, Ph.D

    J. Hoppe,Quantum Theory of a Massless Relativistic Surface and a Two-Dimensional Bound State Problem, Ph.D. Thesis, MIT (1982)

    work page 1982

  15. [15]

    Diffeomorphism Groups, Quantization, andSU(∞),

    J. Hoppe, “Diffeomorphism Groups, Quantization, andSU(∞),” Int. J. Mod. Phys. A4, 5235 (1989)

    work page 1989

  16. [16]

    de Wit, J

    B. de Wit, J. Hoppe and H. Nicolai,On the Quantum Mechanics of Supermembranes, Nucl. Phys. B305, 545 (1988)

    work page 1988

  17. [17]

    Vacuum States in Supersymmetric Kaluza-Klein Theory,

    J. Kowalski-Glikman, “Vacuum States in Supersymmetric Kaluza-Klein Theory,” Phys. Lett. B134, 194-196 (1984)

    work page 1984

  18. [18]

    A New maximally supersymmetric background of IIB superstring theory,

    M. Blau, J. M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, “A New maximally supersymmetric background of IIB superstring theory,” JHEP01, 047 (2002) [arXiv:hep- th/0110242 [hep-th]]

    work page arXiv 2002

  19. [19]

    Azeyanagi, M

    T. Azeyanagi, M. Hanada, T. Hirata and H. Shimada,On the Shape of a D-Brane Bound State and Its Topology Change, J. High Energy Phys.0903, 121

    work page

  20. [20]

    Zwiebach,A First Course in String Theory, 2nd ed., Cambridge University Press, Cambridge (2009)

    B. Zwiebach,A First Course in String Theory, 2nd ed., Cambridge University Press, Cambridge (2009)

    work page 2009

  21. [21]

    Becker, M

    K. Becker, M. Becker and J. H. Schwarz,String Theory and M-Theory: A Modern Intro- duction(Cambridge University Press, Cambridge, 2006)

    work page 2006

  22. [22]

    J. M. Maldacena,The LargeNLimit of Superconformal Field Theories and Supergravity, Adv. Theor. Math. Phys.2, 231 (1998) [Int. J. Theor. Phys.38, 1113 (1999)], arXiv:hep- th/9711200

    work page arXiv 1998

  23. [23]

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov,Gauge Theory Correlators from Non- Critical String Theory, Phys. Lett. B428, 105 (1998), arXiv:hep-th/9802109. 94

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  24. [24]

    Anti De Sitter Space And Holography

    E. Witten,Anti-de Sitter Space and Holography, Adv. Theor. Math. Phys.2, 253 (1998), arXiv:hep-th/9802150

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  25. [25]

    Confinement of Quarks,

    K. G. Wilson, “Confinement of Quarks,” Phys. Rev. D10, 2445-2459 (1974)

    work page 1974

  26. [26]

    Black hole thermodynamics from simulations of lattice Yang–Mills theory,

    Catterall, S. and Wiseman, T., “Black hole thermodynamics from simulations of lattice Yang–Mills theory,”Phys. Rev. D78, 041502 (2008)

    work page 2008

  27. [27]

    Monte Carlo stud- ies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite tem- perature,

    Anagnostopoulos, K. N., Hanada, M., Nishimura, J. and Takeuchi, S., “Monte Carlo stud- ies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite tem- perature,”Phys. Rev. Lett.100, 021601 (2008)

    work page 2008

  28. [28]

    Holographic description of quantum black hole on a computer,

    Hanada, M., Hyakutake, Y., Ishiki, G. and Nishimura, J., “Holographic description of quantum black hole on a computer,”Science344, 882 (2014)

    work page 2014

  29. [29]

    Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finiteN,

    Hanada, M., Hyakutake, Y., Ishiki, G. and Nishimura, J., “Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finiteN,”Phys. Rev. D94, 086010 (2016)

    work page 2016

  30. [30]

    The BFSS model on the lattice

    V. G. Filev and D. O’Connor, “The BFSS model on the lattice,” JHEP1605, 167 (2016) [arXiv:1506.01366 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  31. [31]

    Black hole thermodynamics from calculations in strongly coupled gauge theory,

    Kabat, D. N., Lifschytz, G. and Lowe, D. A., “Black hole thermodynamics from calculations in strongly coupled gauge theory,”Phys. Rev. Lett.86, 1426 (2001)

    work page 2001

  32. [32]

    Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics,

    Hanada, M., Hyakutake, Y., Nishimura, J. and Takeuchi, S., “Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics,”Phys. Rev. Lett.102, 191602 (2009)

    work page 2009

  33. [33]

    Quantum near-horizon geometry of a black 0-brane,

    Y. Hyakutake, “Quantum near-horizon geometry of a black 0-brane,”Progr. Theor. Exp. Phys.2014, 033B04 (2014)

    work page 2014

  34. [34]

    Hanada,What Lattice Theorists Can Do for Superstring/M-Theory, Int

    M. Hanada,What Lattice Theorists Can Do for Superstring/M-Theory, Int. J. Mod. Phys. A31, 1643006 (2016)

    work page 2016

  35. [35]

    Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills

    D. E. Berenstein, J. M. Maldacena and H. S. Nastase, “Strings in flat space and pp waves from N=4 superYang-Mills,” JHEP04, 013 (2002) [arXiv:hep-th/0202021 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  36. [36]

    Massive super Yang-Mills quantum mechanics: Classification and the relation to supermembrane,

    N. Kim and J. H. Park, “Massive super Yang-Mills quantum mechanics: Classification and the relation to supermembrane,” Nucl. Phys. B759, 249–282 (2006) [arXiv:hep- th/0607005]

    work page arXiv 2006

  37. [37]

    Noncriticalosp(1|2,R) M-theory matrix model with an arbitrary time- dependent cosmological constant,

    J. H. Park, “Noncriticalosp(1|2,R) M-theory matrix model with an arbitrary time- dependent cosmological constant,” Nucl. Phys. B745, 123–141 (2006) [arXiv:hep- th/0510070]. 95

    work page arXiv 2006

  38. [38]

    Dielectric-Branes

    R. C. Myers, “Dielectric-branes,” JHEP12, 022 (1999) [arXiv:hep-th/9910053 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  39. [39]

    Bubbling AdS space and 1/2 BPS geometries

    H. Lin, O. Lunin and J. M. Maldacena, “Bubbling AdS space and 1/2 BPS geome- tries,” JHEP10, 025 (2004) doi:10.1088/1126-6708/2004/10/025 [arXiv:hep-th/0409174 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2004/10/025 2004

  40. [40]

    Gauged permutation invariant matrix quantum mechanics: Path Integrals

    D. O’Connor and S. Ramgoolam, “Gauged permutation invariant matrix quantum me- chanics: path integrals,” JHEP04, 080 (2024) [arXiv:2312.12397 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  41. [41]

    Permutation invariant matrix quantum thermodynamics and negative specific heat capacities in large N systems

    D. O’Connor and S. Ramgoolam, “Permutation invariant matrix quantum thermody- namics and negative specific heat capacities in large N systems,” JHEP12, 161 (2024) [arXiv:2405.13150 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  42. [42]

    Phases of one dimensional large N gauge theory in a 1/D expansion

    G. Mandal, M. Mahato and T. Morita, “Phases of one dimensional large N gauge theory in a 1/D expansion,” JHEP1002(2010) 034 doi:10.1007/JHEP02(2010)034 [arXiv:0910.4526 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep02(2010)034 2010

  43. [43]

    Phases of a two dimensional large N gauge theory on a torus

    G. Mandal and T. Morita, “Phases of a two dimensional large N gauge theory on a torus,” Phys. Rev. D84, 085007 (2011) doi:10.1103/PhysRevD.84.085007 [arXiv:1103.1558 [hep- th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.84.085007 2011

  44. [44]

    Black Hole Thermodynamics from Calculations in Strongly-Coupled Gauge Theory

    D. N. Kabat, G. Lifschytz and D. A. Lowe, “Black hole thermodynamics from calculations in strongly coupled gauge theory,” Int. J. Mod. Phys. A16, 856 (2001) [Phys. Rev. Lett. 86, 1426 (2001)] [hep-th/0007051]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  45. [45]

    Black hole entropy from non-perturbative gauge theory

    D. N. Kabat, G. Lifschytz and D. A. Lowe, “Black hole entropy from nonperturbative gauge theory,” Phys. Rev. D64, 124015 (2001) [hep-th/0105171]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  46. [46]

    Phase structure of matrix quantum mechanics at finite temperature

    N. Kawahara, J. Nishimura and S. Takeuchi, “Phase structure of matrix quantum mechan- ics at finite temperature,” JHEP0710, 097 (2007) [arXiv:0706.3517 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  47. [47]

    Possible Third Order Phase Transition in the Large N Lattice Gauge Theory,

    D. J. Gross and E. Witten, “Possible Third Order Phase Transition in the Large N Lattice Gauge Theory,” Phys. Rev. D21, 446 (1980)

    work page 1980

  48. [48]

    N = Infinity Phase Transition in a Class of Exactly Soluble Model Lattice Gauge Theories,

    S. R. Wadia, “N = Infinity Phase Transition in a Class of Exactly Soluble Model Lattice Gauge Theories,” Phys. Lett.93B, 403 (1980)

    work page 1980

  49. [49]

    Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle

    O. Aharony, J. Marsano, S. Minwalla and T. Wiseman, “Black hole-black string phase transitions in thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle,” Class. Quant. Grav.21, 5169-5192 (2004) [arXiv:hep-th/0406210 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  50. [50]

    The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories

    O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, “The Hagedorn - deconfinement phase transition in weakly coupled large N gauge theories,” Adv. Theor. Math. Phys.8, 603 (2004) doi:10.4310/ATMP.2004.v8.n4.a1 [hep-th/0310285]. 96

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.4310/atmp.2004.v8.n4.a1 2004

  51. [51]

    Finite temperature effective action, AdS_5 black holes, and 1/N expansion

    L. Alvarez-Gaume, C. Gomez, H. Liu and S. Wadia, “Finite temperature effective action, AdS(5) black holes, and 1/N expansion,” Phys. Rev. D71, 124023 (2005) [hep-th/0502227]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  52. [52]

    D. A. Cox, J. B. Little and D. O’Shea,Using Algebraic Geometry, 2nd ed., Springer, New York (2005), pp. 295–298

    work page 2005

  53. [53]

    The non-perturbative phase diagram of the BMN matrix model

    Y. Asano, V. G. Filev, S. Kov´ aˇ cik and D. O’Connor, “The non-perturbative phase diagram of the BMN matrix model,” JHEP07, 152 (2018) [arXiv:1805.05314 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  54. [54]

    The Confining Transition in the Bosonic BMN Matrix Model

    Y. Asano, S. Kov´ aˇ cik and D. O’Connor, “The Confining Transition in the Bosonic BMN Matrix Model,” JHEP06, 174 (2020) [arXiv:2001.03749 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  55. [55]

    Differential Operators on a Semisimple Lie Algebra,

    Harish-Chandra, “Differential Operators on a Semisimple Lie Algebra,” Am. J. Math.79, no.1, 87 (1957)

    work page 1957

  56. [56]

    The Planar Approximation. 2.,

    C. Itzykson and J. B. Zuber, “The Planar Approximation. 2.,” J. Math. Phys.21, 411 (1980)

    work page 1980

  57. [57]

    WKB-expansion of the HarishChandra-Itzykson-Zuber integral for arbitrary beta

    S. Hikami and E. Brezin, “WKB-Expansion of the HarishChandra-Itzykson-Zuber Integral for Arbitraryβ,” Prog. Theor. Phys.116, no.3, 441-502 (2006) [arXiv:math-ph/0604041 [math-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  58. [58]

    An extension of the HarishChandra-Itzykson-Zuber integral

    E. Br´ ezin and S. Hikami, “An extension of the Harish-Chandra–Itzykson–Zuber integral,” arXiv:math-ph/0208002

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [59]

    On the Variation in the cohomology of the sym- plectic form of the reduced phase space,

    J. J. Duistermaat and G. J. Heckman, “On the Variation in the cohomology of the sym- plectic form of the reduced phase space,” Invent. Math.69, 259-268 (1982)

    work page 1982

  60. [60]

    Recursive Construction for a Class of Radial Functions I - Ordinary Space

    T. Guhr and H. Kohler, “Recursive Construction for a Class of Radial Functions I – Ordinary Space,” arXiv:math-ph/0011007

    work page internal anchor Pith review Pith/arXiv arXiv

  61. [61]

    Random matrix theories in quantum physics: Common concepts,

    T. Guhr, A. Muller-Groeling and H. A. Weidenmuller, “Random matrix theories in quantum physics: Common concepts,” Phys. Rept.299, 189-425 (1998) [arXiv:cond- mat/9707301 [cond-mat]]

    work page arXiv 1998

  62. [62]

    The distribution of the latent roots of the covariance matrix,

    A. T. James, “The distribution of the latent roots of the covariance matrix,” Ann. Math. Stat.31, 151 (1960)

    work page 1960

  63. [63]

    The distribution of the latent roots of the covariance matrix (II),

    A. T. James, “The distribution of the latent roots of the covariance matrix (II),” Ann. Math. Stat.32, 874 (1961)

    work page 1961

  64. [64]

    Distributions of matrix variates and latent roots derived from normal sam- ples,

    A. T. James, “Distributions of matrix variates and latent roots derived from normal sam- ples,” Ann. Math. Stat.35, 475 (1965)

    work page 1965

  65. [65]

    The Generalised Product Moment Distribution in Samples from a Normal Multivariate Population,

    J. Wishart, “The Generalised Product Moment Distribution in Samples from a Normal Multivariate Population,” Biometrika20A, 32 (1928). 97

    work page 1928

  66. [66]

    Richtungsfelder und Fernparallelismus inn-dimensionalen Mannigfaltigkeiten,

    E. Stiefel, “Richtungsfelder und Fernparallelismus inn-dimensionalen Mannigfaltigkeiten,” Comment. Math. Helv.8, 305 (1935/36)

    work page 1935

  67. [67]

    Normal Multivariate Analysis and the Orthogonal Group,

    A. T. James, “Normal Multivariate Analysis and the Orthogonal Group,” Ann. Math. Stat.25, 40 (1954)

    work page 1954

  68. [68]

    Bessel Functions of Matrix Argument,

    C. S. Herz, “Bessel Functions of Matrix Argument,” Ann. Math.61, 474 (1955)

    work page 1955

  69. [69]

    Distributions of Matrix Variates and Latent Roots Derived from Normal Samples,

    A. T. James, “Distributions of Matrix Variates and Latent Roots Derived from Normal Samples,” Ann. Math. Stat.35, 475 (1964)

    work page 1964

  70. [70]

    R. J. Muirhead,Aspects of Multivariate Statistical Theory, Wiley, New York (1982)

    work page 1982

  71. [71]

    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, 467-491 (1997) [arXiv:hep-th/9612115 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  72. [72]

    The QM/NCG Correspondence

    B. Ydri, “The QM/NCG Correspondence,” doi:10.1142/9789811270437 0027 [arXiv:2211.00339 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/9789811270437

  73. [73]

    Quantized Noncommutative Geometry from Multitrace Matrix Models

    B. Ydri, R. Khaled and C. Soudani, “Quantized noncommutative geometry from multitrace matrix models,” Int. J. Mod. Phys. A37, no.10, 2250052 (2022) doi:10.1142/S0217751X2250052X [arXiv:2110.06677 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x2250052x 2022

  74. [74]

    Two approaches to quantum gravity and M-(atrix) theory at large number of dimensions

    B. Ydri, “Two approaches to quantum gravity and M-(atrix) theory at large number of dimensions,” Int. J. Mod. Phys. A36, no.31n32, 2150234 (2021) doi:10.1142/S0217751X21502341 [arXiv:2007.04488 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x21502341 2021

  75. [75]

    Ydri,unpublished work/work in progress

    B. Ydri,unpublished work/work in progress

    work page

  76. [76]

    A Double--Scaling Large--\(d\) Saddle of BFSS/BMN Matrix Quantum Mechanics

    B. Ydri, “A Double–Scaling Large–dSaddle of BFSS/BMN Matrix Quantum Mechanics,” [arXiv:2606.17758 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv

  77. [77]

    Molien--Weyl Singlet Counting and BFSS$_2$--Factorization in Gaussian Matrix QM

    B. Ydri, “Molien–Weyl Singlet Counting and BFSS 2–Factorization in Gaussian Matrix QM,” [arXiv:2605.04621 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv

  78. [78]

    Ydri,Initiation to Matrix Quantum Gravity and Monte Carlo Simulation of the BFSS3/BMN3 System

    B. Ydri,Initiation to Matrix Quantum Gravity and Monte Carlo Simulation of the BFSS3/BMN3 System

    work page

  79. [79]

    Endpoint formulation and Molien--Weyl structure for the \(N=2\), large--\(d\) BFSS/BMN models

    B. Ydri, “Endpoint formulation and Molien–Weyl structure for theN= 2, large–d BFSS/BMN models,” [arXiv:2605.25647 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv

  80. [80]

    Ydri,Endpoint Entropy and Emergent Grassmannian Geometry in BFSS/BMN Sys- tems

    B. Ydri,Endpoint Entropy and Emergent Grassmannian Geometry in BFSS/BMN Sys- tems

    work page

Showing first 80 references.