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Randomized Wilson loops, reduced models and the large D expansion
High Energy Physics - Theory · Submitted 29 Jan 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting averaged Wilson loop displays a scale behavior strongly reminiscent of the area law.
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The abstract, sentence by sentence
Reduced models are matrix integrals believed to be related to the large N limit of gauge theories. These integrals are known to simplify further when the number of matrices D (corresponding to the number of space-time dimensions in the gauge theory) becomes large. Even though this limit appears to be of little use for computing the standard rectangular Wilson loop (which always singles out two directions out of D), a meaningful large D limit can be defined for a randomized Wilson loop (in which all D directions contribute equally). In this article, a proof-of-concept demonstration of this approach is given for the simplest reduced model (the original Eguchi-Kawai model) and the simplest randomization of the Wilson loop (Brownian sum over random walks). The resulting averaged Wilson loop displays a scale behavior strongly reminiscent of the area law.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Reduced models are matrix integrals believed to be related to the large N limit of gauge theories. | background 1.00 | 0.04 | 0.03 | hedged possibility 0.64 |
| s1 | These integrals are known to simplify further when the number of matrices D (corresponding to the number of space-time dimensions in the gauge theory) becomes large. | background 1.00 | 0.06 | 0.03 | asserted 0.99 |
| s2 | Even though this limit appears to be of little use for computing the standard rectangular Wilson loop (which always singles out two directions out of D), a meaningful large D limit can be defined for a randomized Wilson loop (in which all D directions contribute equally). | contribution 0.44 | 0.23 | 0.25 | asserted 0.92 |
| s3 | In this article, a proof-of-concept demonstration of this approach is given for the simplest reduced model (the original Eguchi-Kawai model) and the simplest randomization of the Wilson loop (Brownian sum over random walks). | contribution 0.91 | 0.93 | 0.11 | asserted 0.98 |
| s4 | The resulting averaged Wilson loop displays a scale behavior strongly reminiscent of the area law. | result 0.97 | 0.91 | 0.66 | asserted 0.86 |
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The paper
Original abstract
Reduced models are matrix integrals believed to be related to the large N limit of gauge theories. These integrals are known to simplify further when the number of matrices D (corresponding to the number of space-time dimensions in the gauge theory) becomes large. Even though this limit appears to be of little use for computing the standard rectangular Wilson loop (which always singles out two directions out of D), a meaningful large D limit can be defined for a randomized Wilson loop (in which all D directions contribute equally). In this article, a proof-of-concept demonstration of this approach is given for the simplest reduced model (the original Eguchi-Kawai model) and the simplest randomization of the Wilson loop (Brownian sum over random walks). The resulting averaged Wilson loop displays a scale behavior strongly reminiscent of the area law.
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What this paper does with the arXiv papers it cites
What it cites · 13 sentences without a confident label
Uses the method or tool of 1 paper
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For the Eguchi-Kawai model, this simplification can be demonstrated by the following technique [ref] .
Dynamical Aspects of Large N Reduced Models · Introduction · 0.93
Compares with 1 paper
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It is instructive to examine our results in the light of numerical findings reported in [ref] .
Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory · Conclusions · 0.92
Cites as background 2 papers
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Reduced models (for a textbook exposition, see [ref] , for a review of more recent developments, see [ref] ) are matrix integrals whose large $N$ limit is related to large $N$ limits of gauge theories.
Large-N reduction in QCD-like theories with massive adjoint fermions · Introduction · 1.00
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Some applications of the high temperature/small volume limit of gauge theories can be found in [ref] .
Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle · Conclusions · 1.00
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