Matrix Perturbation Theory For M-theory On a PP-Wave

Keshav Dasgupta; Mark Van Raamsdonk; Mohammad M. Sheikh-Jabbari

REVIEW

Matrix Perturbation Theory For M-theory On a PP-Wave

Keshav Dasgupta, Mohammad M. Sheikh-Jabbari, Mark Van Raamsdonk

High Energy Physics - Theory · Submitted 19 May 2002 · 26 references

Pith's verdict: A solid, useful BMN follow-up: the exact large-mu spectrum and BPS classification are done properly, and the authors are upfront that the M-theory limit is where it comes apart.

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CitationKeshav Dasgupta, Mark Van Raamsdonk, Mohammad M. Sheikh-Jabbari. "Matrix Perturbation Theory For M-theory On a PP-Wave." arXiv:hep-th/0205185 (2002). https://pith.science/paper/5OM4DCMB

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Editor's note

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Worth your time if you work on the BMN matrix model; skip it if you don't. The core of the paper is section 5: they diagonalize the quadratic action about every classical vacuum in a basis of matrix spherical harmonics and get oscillator masses that are rational multiples of mu and independent of N, with N acting only as a cutoff on j. Tables 1 and 2 are the content people will cite. The check they advertise holds: boson and fermion mass sums agree, so the vacuum zero-point energy cancels. (The stress-test note quotes that sum as (2/9)N(8N^2+1); it's 9/2, a slip in the note, not the paper.) The BPS classification in 5.5 is a direct construction from the oscillator quantum numbers, not an inference from a highest-weight argument, and the dot products come out non-negative with zeros only at m = +/- j. The second-order vacuum energy shift cancelling between quartic and cubic pieces is a genuine check on their perturbation machinery, and the appendix C calculations are laid out well enough to redo by hand. The result that the leading correction about the single-membrane vacuum is finite as N goes to infinity, implying better UV behavior than the Poisson-bracket power counting suggests, is the most interesting thing in the paper and is buried in 7.2. Someone should follow up on it. Soft spots, in order of how much they matter. The M-theory limit problem is real and they know it: appendix D builds explicit paths between the {N+1} and {N,1} vacua with barrier height of order (mu N/R)^3/N, which vanishes at fixed p+ as N grows, so the vacua are not isolated in the limit that defines the theory. They say so in 7.1 and leave the criterion question (g^2 vs g^2 N) open in 6.4. That is honest, and it does not touch the spectrum tables. The D0-brane derivation in section 3 leans on the weak-background action in a regime where the compactified IIA background is singular at F^2 = 4; they flag this in the text and in footnote 7. Minor. The 'complete set of BPS states' is a mu = infinity statement, and which states survive at finite mu is explicitly left for future work in section 8. Also minor: the claim that all BPS states are generated by single rows of (5.11) is argued rather than proved, though it looks right. Send it out. The spectrum and BPS list are correct as far as I can tell and are already load-bearing in the literature.

Referee report

Significance

The spectrum computation in section 5 is clean and internally cross-checked: the sum of boson masses and the sum of fermion masses in table 1 both equal (2/9)N(8N^2+1), as required for vanishing vacuum zero-point energy, and the second-order vacuum energy shift cancels between the quartic and cubic contributions in appendix C.1. The BPS classification in section 5.5 is explicit and complete at µ=∞, with the oscillator list in (5.11) constructed directly rather than inferred from the highest-weight argument. The identification of the effective coupling λ=g^2K in section 6.4 and the explicit construction of paths between vacua in appendix D are useful results that frame subsequent work on the BMN model. The paper provides a well-defined perturbative framework and a complete leading-order spectrum that has been widely used in the field.

Major objections (2)

[Section 3 and abstract] The D0-brane derivation in section 3 is valid only in the weak-curvature region F^2 << 4, where the type IIA background (3.4)-(3.6) is well defined; the authors themselves note that the background becomes singular at F^2=4 and that extending the weak-field D0-brane action to the full model requires an assumption (introduction and section 3.1). The abstract states without qualification that the model 'may be derived ... from the dynamics of D0-branes in type IIA string theory,' which overstates the status of this derivation relative to the supermembrane derivation in section 2. The authors acknowledge the assumption in the body, but the abstract should be qualified to reflect that the D0-brane derivation is valid only in the weakly curved region and that its extension to the full BMN model is assumed rather than shown.
[Sections 6.4 and 7.1] The paper presents two different criteria for the validity of perturbation theory: the explicit calculations in sections 6.2 and 6.3 give g^2 << 1, while the barrier-height estimate in appendix D gives g^2 N << 1. The authors acknowledge the tension in section 6.4 ('Further work will be required to decisively determine which of these conditions ... actually governs the validity of perturbation theory'), but the abstract claims to 'estimate the range of parameters and energies for which perturbation theory is valid' without indicating that the criterion is unsettled. Furthermore, the flat directions connecting vacua constructed in appendix D have maximum energy of order (µN/R)^3/N, which vanishes in the M-theory limit N→∞ at fixed p+=N/R; the authors acknowledge in section 7.1 that the classical vacua are then no longer isolated and that 'it is not clear whether the M-theory limit is compatible with a valid perturbation expansion.' These are real limitations of the claimed results, and the abstract and section 7 should state more explicitly that the perturbative spectrum is established at large µ for fixed N and R, and that its relevance to the M-theory limit is an open question.

Minor objections (6)

[Tables 1 and 2] The symmetry labels in the first column of tables 1 and 2 read 'S0(6)' and 'S0(3)'; these should be 'SO(6)' and 'SO(3)'.
[Section 5.2, equations (5.6)-(5.7) and table 1] The j ranges quoted below equations (5.6) and (5.7) do not match the ranges in table 1: the eigenstate formulas use 0<j<N for the α modes and 0≤j<N for the β modes, while table 1 lists 0≤j≤N-2 for α and 1≤j≤N for β. The shift arises because the labels α_{j-1,m} and β_{j+1,m} in (5.6)-(5.7) refer to the physical spin, but this is not stated. A sentence clarifying the labeling convention would remove the apparent inconsistency.
[Abstract] The abstract states that the paper finds 'the complete (infinite) set of BPS states' without qualifying that this classification is at µ=∞. The body is clear that the BPS analysis is performed in the large-µ limit (section 5.5) and that which states remain BPS at finite µ is left open (section 8). The abstract should carry the same qualification.
[Section 2.1] The regularization prescription at the end of section 2.1 replaces Poisson brackets with commutators and states that the matrix model 'follows immediately.' For the cubic term ǫ_{ijk}{X^i,X^j}X^k, the replacement involves a trace and an ordering choice that is not discussed. A brief remark on the ordering convention would make the derivation self-contained.
[Section 7.2] The discussion of the supermembrane field theory suggests that the theory 'may have much better renormalizability properties than it appears to' and that it 'would be quite interesting if the Poisson bracket field theory turned out to be perturbatively renormalizable.' These are speculative remarks and should be flagged as such rather than presented alongside the established results of sections 5 and 6.
[Section 5.5] The BPS classification is complete at µ=∞, but the paper does not determine which of these states remain BPS at finite µ; this is acknowledged in section 8. A short forward reference in section 5.5 to the discussion in section 8 would help the reader place the result.

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The paper

The paper claims

The pp-wave matrix model of M-theory becomes exactly solvable in the large-mass limit: expanding about any of its fuzzy-sphere vacua gives a quadratic theory whose oscillator masses are rational multiples of the mass parameter $mu$ and do n

The reading

The paper asks whether the matrix model that Berenstein, Maldacena and Nastase proposed for M-theory on the maximally supersymmetric pp-wave can actually be solved, rather than merely written down. Its answer is that the model carries a tunable mass parameter $mu$, and that expanding about any of the model's classical vacua — block-diagonal collections of fuzzy spheres, one collection for each way of partitioning $N$ — leaves a quadratic theory whose interaction terms are suppressed by powers of $R/mu$. Taking $mu to infinity$, the authors diagonalize that quadratic theory exactly in a basis of matrix spherical harmonics and obtain oscillator masses that are rational multiples of $mu$ and completely independent of $N$, with $N$ acting only as a cutoff on the angular momentum of the modes. They then classify every state that preserves some of the 32 supercharges, finding infinite towers preserving 2, 4, 6, 8 and 16 supercharges. The payoff, if the picture holds, is a concrete free spectrum for a single spherical supermembrane in a pp-wave background together with a perturbative handle on how its interactions correct that spectrum.

What carries the argument

The load-bearing device is the expansion of fluctuations in matrix spherical harmonics: the adjoint action of the vacuum generators $J^i$ on an $N times N$ matrix decomposes into integer spins $j = 0, ldots, N-1$, so every quadratic operator in the expanded action becomes diagonal in $(j,m)$ and its eigenvalues reduce to a finite linear-algebra problem in $m$. This is what turns the commutators $[J^i, cdot]$ into numbers, gives masses of the form $mu(j + text{const})/3$, and makes $N$ a cutoff on $j$ rather than a parameter in the masses. The same decomposition, with the Wigner $3j$ and $6j$ symbols controlling products of harmonics, is what makes the cubic and quartic interactions organize into a systematic $1/mu$ expansion with a definite effective coupling per vacuum.

Extended reading notes

Core claim

The central claim is that in the large-$mu$ limit the massive matrix model splits into superselection sectors, one per classical supersymmetric vacuum, and that within each sector the spectrum can be written down exactly. The classical vacua are the solutions $X^i = frac{mu}{3R} J^i$ with $X^a = 0$, where the $J^i$ furnish an $N$-dimensional (possibly reducible) representation of $SU(2)$; geometrically these are sets of fuzzy spheres whose radii are proportional to the light-cone momentum each carries. Expanding about such a vacuum and rescaling fields and time, the quadratic actions for the $SO(3)$ directions, the $SO(6)$ directions and the fermions are diagonalized in a basis of matrix spherical harmonics, and the resulting masses are $frac{mu}{3}(j + frac12)$ for the $SO(6)$ bosons, $frac{mu}{3}(j+1)$ and $frac{mu}{3}j$ for the two $SO(3)$ towers, and $frac{mu}{3}(j + frac34)$, $frac{mu}{3}(j + frac14)$ for the two fermion towers, with $j$ bounded by $N$ and, for reducible vacua, by the pair of block dimensions. Because the masses do not depend on $N$, the large-$N$ limit is a genuine continuum limit of the quadratic supermembrane theory. From this spectrum the authors read off the complete set of BPS states of the $mu = infty$ theory, organized by which of the sixteen supercharges $Q$ each oscillator commutes with, and they identify the states preserving 2, 4, 6, 8 and 16 supercharges. They then compute explicit second-order energy shifts for the lowest non-BPS states, finding that the correction is controlled by an effective coupling $g^2 K$ — where $g = (R/(mu N_1))^{3/2}$ is the bare coupling of a vacuum built from spheres of size $N_1$ and $K$ is the multiplicity — so that the single-membrane vacuum has coupling $(R/(mu N))^3$ and the $X=0$ vacuum has $(R/mu)^3$.

Load-bearing premise

The load-bearing premise is that expanding about a single vacuum at large $mu$ remains a controlled starting point for the M-theory limit — the limit of large $N$ at fixed $p^+ = N/R$ and fixed $mu$ — even though the paper's own appendix shows the barriers separating vacua shrink like $(mu N/R)^3/N$ and the authors state in section 7.1 that the vacua become connected by flat directions in that limit.

Editorial extensions

If this is right

The quadratic spectrum about the irreducible vacuum can be read as the free spectrum of a single spherical supermembrane in the pp-wave background, with $N$ playing the role of a short-distance cutoff on the mode number.
Coincident membranes produce $K^2$ copies of a single-membrane spectrum, and membranes of different sizes have off-diagonal modes whose masses grow like $mu|N_1 - N_2|/2$, giving a matrix-model account of non-abelian membrane structure.
The complete BPS catalogue at $mu = infty$ supplies the list of candidate protected states whose energies, if they survive at finite $mu$, are fixed exactly by their angular momenta.
The effective couplings differ by vacuum, with the single-membrane vacuum the weakest coupled, so perturbation theory is most trustworthy for a large membrane and least trustworthy near $X = 0$.
In the strict large-$N$, fixed-$p^+$ limit the potential barriers between vacua are computed to scale like $(mu N/R)^3/N$, so the classical vacua cease to be isolated and the model develops flat directions connecting them.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same harmonic decomposition should apply essentially unchanged to the type IIB pp-wave matrix model built from D3-brane giant gravitons, so a parallel exact free spectrum and BPS catalogue ought to exist there, with the sphere radius replaced by the sum of squared radii.
The vanishing barrier height in the M-theory limit is a statement about the supermembrane worldvolume theory as much as about the matrix model: the flat directions correspond to singular domain walls or tensionless strings on the membrane, which suggests the continuum field theory is not a conventional weakly coupled gauge theory at all.
The tension between the two validity criteria — $g^2 ll 1$ from explicit low-lying energy shifts versus $g^2 N ll 1$ from barrier heights — looks resolvable by a more careful accounting of phase space: the low-barrier paths are narrow, so a saddle-point or density-of-paths estimate could decide which condition actually controls the breakdown.
The $N$-independence of the oscillator masses suggests that the free spectrum is a fixed feature of the pp-wave background rather than of the regularization, so a direct continuum light-cone quantization of the supermembrane in this background should reproduce the same tower.

Original abstract

In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamics of D0-branes in type IIA string theory. We consider expanding the model about each of its classical supersymmetric vacua and note that for large values of the mass parameter \mu, interaction terms are suppressed by powers of 1/mu, so that the model may be studied in perturbation theory. We compute the exact spectrum about each of the vacua in the large \mu limit and find the complete (infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or 16 supercharges. Through explicit perturbative calculations, we then determine the effective coupling that controls the perturbation expansion for large \mu and estimate the range of parameters and energies for which perturbation theory is valid.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,523 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.48 · compares with prior results 0.29 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamics of D0-branes in type IIA string theory. We consider expanding the model about each of its classical supersymmetric vacua and note that for large values of the mass parameter \mu, interaction terms are suppressed by powers of 1/mu, so that the model may be studied in perturbation theory. We compute the exact spectrum about each of the vacua in the large \mu limit and find the complete (infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or 16 supercharges. Through explicit perturbative calculations, we then determine the effective coupling that controls the perturbation expansion for large \mu and estimate the range of parameters and energies for which perturbation theory is valid.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave.	contribution 0.60	0.75	0.04	asserted 0.90
s1	We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamics of D0-branes in type IIA string theory.	contribution 0.52	0.84	0.11	hedged possibility 0.86
s2	We consider expanding the model about each of its classical supersymmetric vacua and note that for large values of the mass parameter \mu, interaction terms are suppressed by powers of 1/mu, so that the model may be studied in perturbation theory.	method 0.85	0.83	0.08	asserted 0.56
s3	We compute the exact spectrum about each of the vacua in the large \mu limit and find the complete (infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or 16 supercharges.	result 0.99	0.96	0.40	asserted 1.00
s4	Through explicit perturbative calculations, we then determine the effective coupling that controls the perturbation expansion for large \mu and estimate the range of parameters and energies for which perturbation theory is valid.	contribution 0.49	0.96	0.20	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v4

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Regime of validity for perturbation theory (conservative

**Figure 2.** Low energy path between nearby vacua We expect this estimate to be true for a generic direction away from the minimum However, it turns out that for certain paths away from the minimum, the interaction terms can become important at a much lower energy. In appendix D, we provide an explicit path between the irreducible vacuum labeled by N and the nearby vacuum labeled by (N − 1, 1) along which the maximum energy is of order (µN/R) 3 1 N = 1 g 2N rather than 1/g2 . 15 This path corresponds to the discretized version of a continuum picture in which a thin tube of membrane extends f

Figures reproduced from arXiv:hep-th/0205185 by the authors.

References

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Matrix Theory of Type IIB Plane Wave from Membranes
hep-th 2008-04 conditional novelty 6.0 of 10

A one-parameter massive deformation of the Bagger-Lambert 3-algebra field theory is shown to carry the Type IIB plane wave superalgebra on R x T^2, and is proposed as that background's DLCQ Matrix theory.
Matrix Model in a Class of Time Dependent Supersymmetric Backgrounds
hep-th 2006-03 conditional novelty 6.0 of 10

A matrix model for a class of time-dependent supersymmetric M-theory backgrounds is constructed by membrane regularization, and the action is argued to be exact to all orders in fermions, with fuzzy sphere solutions t...
Fivebranes from gauge theory
hep-th 2005-09 conditional novelty 6.0 of 10

The paper gives a unified construction of gravity duals for several sixteen-supercharge gauge theories and derives their near-BPS string spectra, including a (4,4) sigma model with non-central charges.
BMN Spread Complexity Across Phase Transitions
hep-th 2026-08 conditional novelty 5.0 of 10

The spread complexity of states in the BMN matrix model transitions from quadratic to exponential growth as temperature increases, with a sub-exponential correction from mass-gap bound states at intermediate temperatures.
Krylov complexity and spectral density of BMN matrix model
hep-th 2026-07 reject novelty 5.0 of 10

Using Krylov techniques on the BMN matrix model, the paper derives moment and spectral-function structures at large mass, claiming IR-divergent spectral density and linear entropy growth.
BPS Non-Renormalization in the BMN Matrix Model
hep-th 2026-06 unverdicted novelty 5.0 of 10

Conjugation deformations preserve normalizability in the BMN matrix model, implying BPS states do not lift and their unsigned number is invariant except at the free and BFSS points.
Chaos in the BMN matrix model
hep-th 2015-03 conditional novelty 5.0 of 10

Two consistent truncations of the bosonic BMN matrix model show chaotic Poincare sections and positive Lyapunov exponents, so the full model is not Liouville-integrable, while a third truncation is integrable.
Perturbations in Chromo-Natural Inflation
hep-th 2013-05 conditional novelty 5.0 of 10

Chromo-Natural Inflation generates a chiral, exponentially enhanced gravitational wave spectrum and, in its original form, cannot fit the Planck tilt and tensor-to-scalar ratio at the same time.
Multi-Matrix Quantum Mechanics, Collective Fields and Emergent Space
hep-th 2026-05 unverdicted novelty 4.0 of 10

Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution.
Turbulent aspects of BMN membrane dynamics
hep-th 2024-12 conditional novelty 4.0 of 10

The authors derive leading-order radial and angular stability spectra for two spherical BMN membrane configurations and demonstrate that next-to-leading-order couplings transfer dipole and quadrupole instabilities to ...

How later papers used it

62 later papers cite it

Evidence: substantial. 57 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 27 of the 124 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

5 later papers by other authors are listed below: 3 used its method or tool and 2 compared their own results with it.

Uses its method or tool 3 of 4 papers with this label

Rescaled the fluctuations and parameters following this paper to factor the powers of μ out of the action.

Probing Smearing Effect by Point-Like Graviton in Plane-Wave Matrix Model (2010) · 1.00 · paraphrased: the licence does not allow quoting
Based its procedure of diagonalization on this paper's mode expansion and the standard SU(2) algebra.

Smearing Effect in Plane-Wave Matrix Model (2008) · 0.95 · paraphrased: the licence does not allow quoting
Found the normal modes proceeding as in this paper.

Deep Quantum Geometry of Matrices (2019) · 0.99 · paraphrased: the licence does not allow quoting

Compares with it 2 of 4 papers with this label

Said its results nicely reproduce the ones found in the case of the BMN matrix model in this paper.

Turbulent aspects of BMN membrane dynamics (2024) · 1.00 · paraphrased: the licence does not allow quoting
Said its results are in agreement with those of this paper.

Multipole Stability of Spinning M2-branes in the Classical Limit of the BMN Matrix Model (2017) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

58 arXiv papers cite this in 120 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 77 sentences without a confident label

Uses its method or tool 4 papers

For this purpose, following [ref] , we rescale the fluctuations and parameters as [equation] Under this rescaling, the powers of $μ$ are factored out from the action $S$ in the background ([ref]) and ([ref]) as [equation] where $S_0$, $S_2$, $S_3$ and $S_4$ do not have $μ$ dependence.

Probing Smearing Effect by Point-Like Graviton in Plane-Wave Matrix Model · Background configuration · 1.00
The procedure of diagonalization has been well established based on the mode expansion ([ref]) and the standard $SU(2)$ algebra [ref] .

Smearing Effect in Plane-Wave Matrix Model · Bosonic sector · 0.95
The explicit decomposition into eigenstates is provided by a variant of the usual fuzzy spherical harmonics which provides a basis for rectangular matrices as opposed to square matrices [ref] .

The spectrum of defect ABJM theory · The easy bosons · 0.90

Compares with it 4 papers

While there is no notion of energy scale in the matrix integral (see [ref]), an analogous cavity is seen in the IIA geometry dual to BMN matrix quantum mechanics [ref] .

The Polarised IKKT Matrix Model · Summary of the solution · 0.91
Our results nicely reproduce the ones which were found in the case of the BMN matrix model in [ref] .

Turbulent aspects of BMN membrane dynamics · $SO(3)$ sector · 1.00
which coincide with the eigenvalues that were found in [ref] for the BMN matrix model.

Cascade of instabilities in the classical limit of the BMN matrix model · Eigenvalues · 0.96

Cites it as support 1 paper

Hence they are also quantum mechanically stable at least at perturbative level [ref] .

A non-perturbative formulation of N=4 super Yang-Mills theory based on the large-N reduction · $N=4$ SYM on $R×S^3$ from PWMM · 0.98

Cites it as background 26 papers

The explicit form of the $Y^a_lm$ modes and $ω_lm$ frequencies for the fuzzy sphere state of the Hamiltonian [ref] has recently been discussed in [ref] , building on [ref] .

Minimal Areas from Entangled Matrices · Quantum mechanical state · 0.81
BMN matrix model [ref] was originally conceived as a realization of M theory on a supersymmetric pp wave background in eleven dimensions [ref] , which turns out to be massive deformation of BFSS matrix model [ref] .

Krylov complexity for Lin-Maldacena geometries and their holographic duals · Introduction and General Idea · 0.99
In the context of M-theory, these membranes arise from the BMN matrix model in the limit of large matrix dimensions [ref] .

Cascade of instabilities in the classical limit of the BMN matrix model · Introduction · 0.80

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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