High Energy Physics - Phenomenology · arXiv:1206.1779 v2 · submitted 8 Jun 2012
Solving the Ghost-Gluon System of Yang-Mills Theory on GPUs
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“Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code.”
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Abstract
We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA(TM). Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well-suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.96
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.55 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.86 · mentions code or data availability 0.03
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). | contribution 0.97 | 0.95 | 0.14 | asserted 1.00 |
| Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. | method 0.99 | 0.84 | 0.04 | asserted 0.99 |
| With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. | method 1.00 | 0.88 | 0.04 | asserted 1.00 |
| The resulting Newton matrix is generated in parallel using OpenMPI and CUDA(TM). | method 1.00 | 0.92 | 0.04 | asserted 1.00 |
| Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. | result 1.00 | 0.96 | 0.54 | asserted 0.96 |
| This makes the proposed techniques well-suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. | interpretation 0.93 | 0.50 | 0.28 | asserted 0.75 |
| In addition, the computation of Schwinger functions using GPU devices is studied. | contribution 0.98 | 0.80 | 0.04 | asserted 0.81 |
What kind of paper the classifier reports this is: method or tool 0.86 · evidence from simulation or computation 1.00
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,535 input tokens, $0.0002 reported.
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Reviewed papers on Pith that cite this one. The full citation record
How the literature uses it
6 arXiv papers cite this in 8 sentences
Papers citing it · 4 sentences without a confident label
Builds on it 1 paper
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The starting point is the coupled system of the quark propagator and quark-gluon vertex DSE at vanishing temperatures in the Landau gauge using as input for the gluon propagator either fits [ref] or results from a self-consistent treatment of the corresponding system of DSEs [ref] .[These fits correspond to a so-called scaling solution, one of two solution types of Landau gauge Green functions when classified by their infrared properties, see e.g., ref.
The Quark-Gluon Vertex in Landau gauge QCD · Motivation · 0.91
Uses its method or tool 3 papers
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The gluon propagator $D^μν(p)$ is included self-consistently by solving the corresponding DSEs for the Yang-Mills system[The numerical implementation is detailed in Refs. [ref] .], where we employ the truncation scheme proposed in Refs. [ref] .
Infrared behaviour of propagators and running coupling in the conformal window of QCD · The Coupled System · 1.00
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For the Yang-Mills part the numerical routines proposed in Ref. [ref] have been adopted as well as improved in order to allow for an arbitrary number of GPU devices.
On the Landau gauge matter-gluon vertex in scalar QCD in a functional approach · Numerical treatment · 0.97
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We will improve on this shortcoming via transporting these numerical calculations onto GPUs along the lines of Ref. [ref] .
Including four-gluon interactions into Landau and maximally-Abelian gauge Dyson-Schwinger studies · A model for the four-gluon vertex dressing · 0.97
What it cites · 19 sentences without a confident label
Uses the method or tool of 1 paper
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For the purpose of this numerical study it is sufficient to replace the dressed ghost-gluon vertex by its bare counterpart, i.e. $Γ_ν(q,p)=iq_ν$, whereas for the three-gluon vertex the model proposed in [ref] is employed [equation] with $k^2≡(q-p)^2$.
Non-perturbative Propagators, Running Coupling and Dynamical Mass Generation in Ghost-Antighost Symmetric Gauges in QCD · The Dyson-Schwinger Equations for the Ghost-Gluon System · 0.98
Cites as support 3 papers
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This picture is also enforced by results obtained from lattice simulations, see, e.g., [ref] and references therein, or Functional Renormalization Group methods [ref] .
Further Investigation of Massive Landau-Gauge Propagators in the Infrared Limit · Introduction · 0.97
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This picture is also enforced by results obtained from lattice simulations, see, e.g., [ref] and references therein, or Functional Renormalization Group methods [ref] .
Gauge bosons at zero and finite temperature · Introduction · 0.97
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This picture is also enforced by results obtained from lattice simulations, see, e.g., [ref] and references therein, or Functional Renormalization Group methods [ref] .
Infrared behaviour and fixed points in Landau gauge QCD · Introduction · 0.97
Cites as background 3 papers
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The Dyson-Schwinger (or generally a Green's functions) approach provides a continuum formulation of QCD [ref] capable to describe the system over the entire momentum range.
The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States · Introduction · 0.92
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The Dyson-Schwinger (or generally a Green's functions) approach provides a continuum formulation of QCD [ref] capable to describe the system over the entire momentum range.
Infrared Properties of QCD from Dyson-Schwinger equations · Introduction · 0.92
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The Dyson-Schwinger (or generally a Green's functions) approach provides a continuum formulation of QCD [ref] capable to describe the system over the entire momentum range.
Dyson-Schwinger equations: a tool for hadron physics · Introduction · 0.92
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