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Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models
High Energy Physics - Theory · Submitted 5 Mar 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition.
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The abstract, sentence by sentence
We present a study of D=4 supersymmetric Yang-Mills matrix models with SO(3) mass terms based on the cohomological approach and the Monte Carlo method. In the bosonic models we show the existence of an exotic first/second order transition from a phase with a well defined background geometry (the fuzzy sphere) to a phase with commuting matrices with no geometry in the sense of Connes. At the transition point the sphere expands abruptly to infinite size then it evaporates as we increase the temperature (the gauge coupling constant). The transition looks first order due to the discontinuity in the action whereas it looks second order due to the divergent peak in the specific heat. The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition. The transition point is found to scale to zero with N. We conjecture that the transition from the background sphere to the phase of commuting matrices is associated with spontaneous supersymmetry breaking. The eigenvalues distribution of any of the bosonic matrices in the matrix phase is found to be given by a non-polynomial law obtained from the fact that the joint probability distribution of the four matrices is uniform inside a solid ball with radius R. The eigenvalues of the gauge field on the background geometry are also found to be distributed according to this non-polynomial law. We also discuss the D=3 models and by using cohomological deformation, localization techniques and the saddle-point method we give a derivation of the D=3 eigenvalues distribution starting from a particular D=4 model.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a study of D=4 supersymmetric Yang-Mills matrix models with SO(3) mass terms based on the cohomological approach and the Monte Carlo method. | contribution 0.96 | 0.93 | 0.05 | asserted 0.93 |
| s1 | In the bosonic models we show the existence of an exotic first/second order transition from a phase with a well defined background geometry (the fuzzy sphere) to a phase with commuting matrices with no geometry in the sense of Connes. | result 0.99 | 0.94 | 0.24 | asserted 1.00 |
| s2 | At the transition point the sphere expands abruptly to infinite size then it evaporates as we increase the temperature (the gauge coupling constant). | result 0.98 | 0.84 | 0.09 | asserted 1.00 |
| s3 | The transition looks first order due to the discontinuity in the action whereas it looks second order due to the divergent peak in the specific heat. | result 0.54 | 0.87 | 0.08 | asserted 0.98 |
| s4 | The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition. | result 0.99 | 0.85 | 0.40 | asserted 1.00 |
| s5 | The transition point is found to scale to zero with N. | result 1.00 | 0.92 | 0.09 | asserted 1.00 |
| s6 | We conjecture that the transition from the background sphere to the phase of commuting matrices is associated with spontaneous supersymmetry breaking. | interpretation 1.00 | 0.37 | 0.32 | speculative 1.00 |
| s7 | The eigenvalues distribution of any of the bosonic matrices in the matrix phase is found to be given by a non-polynomial law obtained from the fact that the joint probability distribution of the four matrices is uniform inside a solid ball with radius R. | result 1.00 | 0.94 | 0.09 | asserted 1.00 |
| s8 | The eigenvalues of the gauge field on the background geometry are also found to be distributed according to this non-polynomial law. | result 1.00 | 0.94 | 0.06 | asserted 1.00 |
| s9 | We also discuss the D=3 models and by using cohomological deformation, localization techniques and the saddle-point method we give a derivation of the D=3 eigenvalues distribution starting from a particular D=4 model. | contribution 0.86 | 0.95 | 0.07 | asserted 1.00 |
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The paper
Original abstract
We present a study of D=4 supersymmetric Yang-Mills matrix models with SO(3) mass terms based on the cohomological approach and the Monte Carlo method. In the bosonic models we show the existence of an exotic first/second order transition from a phase with a well defined background geometry (the fuzzy sphere) to a phase with commuting matrices with no geometry in the sense of Connes. At the transition point the sphere expands abruptly to infinite size then it evaporates as we increase the temperature (the gauge coupling constant). The transition looks first order due to the discontinuity in the action whereas it looks second order due to the divergent peak in the specific heat. The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition. The transition point is found to scale to zero with N. We conjecture that the transition from the background sphere to the phase of commuting matrices is associated with spontaneous supersymmetry breaking. The eigenvalues distribution of any of the bosonic matrices in the matrix phase is found to be given by a non-polynomial law obtained from the fact that the joint probability distribution of the four matrices is uniform inside a solid ball with radius R. The eigenvalues of the gauge field on the background geometry are also found to be distributed according to this non-polynomial law. We also discuss the D=3 models and by using cohomological deformation, localization techniques and the saddle-point method we give a derivation of the D=3 eigenvalues distribution starting from a particular D=4 model.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers whose main result relates to this one's
States the same result 1 paper
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The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition.
Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II · 0.98
What it cites · 160 sentences without a confident label
Builds on 2 papers
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Since the ground state configurations are $X_4=0$ and $X_a=αϕL_a$, the theoretical analysis based on the effective potential of the three dimensional model done in [ref] should also hold here largely unchanged (see below).
Matrix Models, Gauge Theory and Emergent Geometry · Bosonic Theory: Emergent Geometry and Phase Diagram · 0.86
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Since the ground state configurations are $X_4=0$ and $X_a=αϕL_a$, the theoretical analysis based on the effective potential of the three dimensional model done in [ref] should also hold here largely unchanged (see below).
Geometry in transition: A model of emergent geometry · Bosonic Theory: Emergent Geometry and Phase Diagram · 0.86
Uses the method or tool of 14 papers
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The critical line can then be obtained following the method of [ref] .
Matrix Models, Gauge Theory and Emergent Geometry · Bosonic Theory: Emergent Geometry and Phase Diagram · 1.00
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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 the nonperturbative dynamics of fuzzy spheres · The Dirac Operator in Simulations · 0.99
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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 $A=N(j_A-1)+i_A$ .
Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory · The Dirac Operator in Simulations · 0.99
Compares with 4 papers
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The eigenvalues distribution we will derive shortly is also different from the one presented in [ref] and it agrees well with the numerical Monte Carlo simulations.
Multi-matrix models and emergent geometry · Saddle-Point Method: The Matrix Phase · 0.96
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We note here the difference between this eigenvalues distribution $ρ_4$ and the eigenvalues distribution of the supersymmetric model with $α̃=β̃=0$ [ref] .
Eigenvalue Distributions in Yang-Mills Integrals · Eigenvalues Distributions · 1.00
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This explicit solution is rather different from the sophisticated implicit solution found in [ref] .
D-particles, Matrix Integrals and KP hierachy · Saddle-Point Method: The Matrix Phase · 0.99
Cites as support 4 papers
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For example we can show in a particular double scaling limit that the nonperturbative phase structure of scalar fields on the Moyal-Weyl plane can be rigorously identified with the nonperturbative phase structure of scalar fields on the fuzzy sphere, and in particular the matrix or nonuniform ordered phase on the fuzzy sphere goes precisely to the stripe phase on the Moyal-Weyl plane [ref] .
Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model · Introduction · 0.97
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This was confirmed in [ref] with the calculation of the one-loop effective potential of the model $YM+CS+V$ on fuzzy $CP_N^2$.
Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2 · Review of Bosonic $D=3$ Yang-Mills Matrix Models · 0.97
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Thus a non-perturbative formulation of non-commutative gauge theory in two dimensions can be captured rigorously within these models [ref] .
Noncommutative Geometry and Gauge Theory on Fuzzy Sphere · Introduction · 0.96
Cites as background 59 papers
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Convergence of Yang-Mills path inetgrals such as the one given by ([ref]) was studied extensively in [ref] and in [ref] .
Eigenvalue Distributions in Yang-Mills Integrals · Path Integral, Convergence and Observables · 0.99
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Convergence of Yang-Mills path inetgrals such as the one given by ([ref]) was studied extensively in [ref] and in [ref] .
Finite Yang-Mills Integrals · Path Integral, Convergence and Observables · 0.99
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Convergence of Yang-Mills path inetgrals such as the one given by ([ref]) was studied extensively in [ref] and in [ref] .
Convergent Yang-Mills Matrix Theories · Path Integral, Convergence and Observables · 0.99
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