Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory

J. Ambjorn; J. Nishimura; K. N. Anagnostopoulos; T. Hotta; W. Bietenholz

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Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory

J. Ambjorn, K. N. Anagnostopoulos, W. Bietenholz, T. Hotta, J. Nishimura

High Energy Physics - Theory · Submitted 23 Mar 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale.

how it is stated · asserted 0.79 read the record →

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arXiv IDhep-th/0003208 (version 1)

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CitationJ. Ambjorn, J. Nishimura, K. N. Anagnostopoulos, T. Hotta, W. Bietenholz. "Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory." arXiv:hep-th/0003208 (2000). https://pith.science/paper/7JRWJ2GL

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.83 · human participants 0.01 · controlled comparison 0.53 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.97 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We perform Monte Carlo simulations of a supersymmetric matrix model, which is obtained by dimensional reduction of 4D SU(N) super Yang-Mills theory. The model can be considered as a four-dimensional counterpart of the IIB matrix model. We extract the space-time structure represented by the eigenvalues of bosonic matrices. In particular we compare the large N behavior of the space-time extent with the result obtained from a low energy effective theory. We measure various Wilson loop correlators which represent string amplitudes and we observe a nontrivial universal scaling in N. We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale. Comparison with the results for the bosonic case clarifies the role of supersymmetry in the large N dynamics. It does affect the multi-point correlators qualitatively, but the Eguchi-Kawai equivalence is observed even in the bosonic case.

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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	We perform Monte Carlo simulations of a supersymmetric matrix model, which is obtained by dimensional reduction of 4D SU(N) super Yang-Mills theory.	method 0.51	0.97	0.04	asserted 1.00
s1	The model can be considered as a four-dimensional counterpart of the IIB matrix model.	background 0.86	0.13	0.04	hedged possibility 0.71
s2	We extract the space-time structure represented by the eigenvalues of bosonic matrices.	contribution 0.53	0.95	0.06	asserted 1.00
s3	In particular we compare the large N behavior of the space-time extent with the result obtained from a low energy effective theory.	contribution 0.64	0.89	0.11	asserted 0.95
s4	We measure various Wilson loop correlators which represent string amplitudes and we observe a nontrivial universal scaling in N.	result 0.95	0.97	0.14	asserted 1.00
s5	We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale.	result 1.00	0.90	0.26	asserted 0.79
s6	Comparison with the results for the bosonic case clarifies the role of supersymmetry in the large N dynamics.	interpretation 0.62	0.82	0.16	asserted 0.97
s7	It does affect the multi-point correlators qualitatively, but the Eguchi-Kawai equivalence is observed even in the bosonic case.	result 0.69	0.81	0.18	asserted 1.00

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

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The paper

Original abstract

We perform Monte Carlo simulations of a supersymmetric matrix model, which is obtained by dimensional reduction of 4D SU(N) super Yang-Mills theory. The model can be considered as a four-dimensional counterpart of the IIB matrix model. We extract the space-time structure represented by the eigenvalues of bosonic matrices. In particular we compare the large N behavior of the space-time extent with the result obtained from a low energy effective theory. We measure various Wilson loop correlators which represent string amplitudes and we observe a nontrivial universal scaling in N. We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale. Comparison with the results for the bosonic case clarifies the role of supersymmetry in the large N dynamics. It does affect the multi-point correlators qualitatively, but the Eguchi-Kawai equivalence is observed even in the bosonic case.

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References

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Cited by 7 Pith papers

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Emergence of a 4D World from Causal Quantum Gravity
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Monte Carlo simulations of four-dimensional causal dynamical triangulations yield an extended quantum geometry whose spatial slices have Hausdorff dimension 3.10 plus or minus 0.15 and whose volume scaling matches a c...
On the strong coupling limit of Yang-Mills matrix models
hep-th 2026-07 conditional novelty 7.0 of 10

In mass-deformed Yang–Mills matrix models, strong-coupling commutativity sets in at or above the critical fermion count N_c = 2(D−2), with the supersymmetric models sitting at the critical boundary where huge-operator...
Bootstrapping Yang-Mills matrix integrals
hep-th 2025-10 conditional novelty 7.0 of 10

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Regularized Master-Field Approximation for Mass-Deformed Supersymmetric Yang-Mills Matrix Models
hep-th 2026-10 conditional novelty 6.0 of 10

The regularized master-field approximation reproduces fuzzy-sphere phases in three mass-deformed supersymmetric matrix models, including the polarised IKKT model, and shows that Dirac zero modes can destabilize the sphere.
Little IIB Matrix Model
hep-th 2006-03 conditional novelty 6.0 of 10

A zero-dimensional matrix model from D=6 pure super Yang-Mills theory is argued to describe the (2,0) Little String Theory at large N, supported by a 1/r^4 force law and (2,0) tensor multiplet vertex operators.

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Late time behaviors of the expanding universe in the IIB matrix model
hep-th 2012-08 conditional novelty 5.0 of 10

A classical solution of the Lorentzian IIB matrix model gives a scale factor whose equation-of-state parameter drifts from -1 to -1/3, offered as a dynamical explanation for the smallness of the cosmological constant.
Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
hep-th 2011-08 conditional novelty 5.0 of 10

A systematic third-order Gaussian-expansion scan of all SO(d) symmetric vacua (2 <= d <= 7) of the type IIB matrix model finds the free energy minimized at d = 3, not d = 4, with a d-independent space-time volume for d >= 3.

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22 arXiv papers cite this in 46 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Eguchi-Kawai equivalence of this model to ordinary gauge theory does hold within a finite range of scale.

Monte Carlo Studies of the Dimensionally Reduced 4d SU(N) Super Yang-Mills Theory · 1.00

Papers citing it · 33 sentences without a confident label

Builds on it 1 paper

The proof is a straightforward generalization of that of the zero-dimensional model [ref] .

Four-dimensional N=1 super Yang-Mills from matrix model · Absence of the sign problem · 0.90

Uses its method or tool 1 paper

Following [ref] , we expand the $N×N$ matrices $θ_1,θ_2$ and $θ_1^+,θ_2^+$ as $θ_i=∑_A=1^N^2θ_i^AT^A$ and $θ_i^+=∑_A=1^N^2(θ_i^A)^*(T^A)^+$ where the $N×N$ matrices $T^A$ are defined by $(T^A)_ij=δ_ii_Aδ_jj_A$ with $i_A$ and $j_A$ are such that $A=N(i_A-1)+j_A$ whereas the matrices $(T^A)^+$ are defined by $(T^A)^+_ij=δ_ii_Aδ_jj_A$ with $i_A$ and $j_A$ such that $A=N(j_A-1)+i_A$ .

Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models · The Dirac Operator in Simulations · 0.99

Compares with it 3 papers

The distances between two points belonging to different configurations are not measured. ] $P(d)$, normalized by the condition $∫dxP(x)=1$, which is consistent with the result of [ref] .

On the shape of a D-brane bound state and its topology change · Distribution of the off-diagonal components and validity of the procedure · 0.96
It is instructive to examine our results in the light of numerical findings reported in [ref] .

Randomized Wilson loops, reduced models and the large D expansion · Conclusions · 0.92
This behavior is reminiscent of the divergence of the second moment in the totally reduced model of 4d $N=1$ super Yang-Mills theory [ref] .

Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature · The models and their basic properties · 0.91

Cites it as support 1 paper

Evidence for the factorization property [ref] in the context of the IIB matrix model has been presented in Ref. [ref] .

IIB matrix model, bosonic master field, and emergent spacetime · Bosonic master field · 0.96

Cites it as background 5 papers

The Euclidean version of the IKKT matrix model and related models, on the other hand, have been studied numerically [ref] since long time before numerical studies of the Lorentzian version were started.

Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model · Introduction · 0.96
These have been studied numerically in for instance [ref] .

Multi-matrix models and emergent geometry · `Supersymmetrised' models · 0.84
For two colors this SUSY theory was studied on the lattice by various authors [ref] (see also the review in Ref. [ref] and the work noted above on the reduced model in the non-compact theory [ref] ).

Non-perturbative volume-reduction of large-N QCD with adjoint fermions · Introduction · 0.97

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