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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 24th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexStarting something. Not done yet, but need to save. <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/1">v1</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

   Starting something. Not done yet, but need to save.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 24th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexnow some minimum in place. <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/1">v1</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

   now some minimum in place.

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 24th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI was just reminded of John Baez years ago [describing](http://math.ucr.edu/home/baez/week92.html) Bar-Natan's paper on the four-color problem and the relation between $SU(2)$ and $SU(n)$ gauge theory. Bar-Natan's paper is [here](https://arxiv.org/abs/q-alg/9606016).

   I was just reminded of John Baez years ago describing Bar-Natan’s paper on the four-color problem and the relation between $SU(2)$ and $SU(n)$ gauge theory. Bar-Natan’s paper is here.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 24th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks, excellent. So let's add that to all related entries: On the [[logical equivalence]] between the [[four-colour theorem]] and a statement about transition from the [[small N limit]] to the [[large N limit]] for [[Lie algebra weight systems]] on [[Jacobi diagrams]] via the [['t Hooft double line construction]]: * [[Dror Bar-Natan]], _Lie Algebras and the Four Color Theorem_, Combinatorica 17-1(1997) 43–52 ([arXiv:q-alg/9606016](https://arxiv.org/abs/q-alg/9606016), [doi:10.1007/BF01196130](https://doi.org/10.1007/BF01196130))

   Thanks, excellent. So let’s add that to all related entries:

   On the logical equivalence between the four-colour theorem and a statement about transition from the small N limit to the large N limit for Lie algebra weight systems on Jacobi diagrams via the ’t Hooft double line construction:

   • Dror Bar-Natan, Lie Algebras and the Four Color Theorem, Combinatorica 17-1(1997) 43–52 (arXiv:q-alg/9606016, doi:10.1007/BF01196130)
5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 24th 2020
   • (edited Jan 24th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI wonder if Bar-Natan didn't know that the double line construction he uses so effectively is earlier due to 't Hooft, or if he intentionally chose to never cite him. Seems a curious omission.

   I wonder if Bar-Natan didn’t know that the double line construction he uses so effectively is earlier due to ’t Hooft, or if he intentionally chose to never cite him. Seems a curious omission.

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 24th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThat would be fun if M-theory could help out with the four-colour problem!

   That would be fun if M-theory could help out with the four-colour problem!

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJan 24th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this pointer on [[1/N corrections]] in [[2d QCD]]: * [[Itzhak Bars]], _QCD and Strings in 2D_ ([arXiv:hep-th/9312018](https://arxiv.org/abs/hep-th/9312018)) <a href="https://ncatlab.org/nlab/revision/diff/large+1%2FN+limit/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/4">v4</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

   added this pointer on 1/N corrections in 2d QCD:

   • Itzhak Bars, QCD and Strings in 2D (arXiv:hep-th/9312018)

   diff, v4, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJan 24th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this pointer: * David Jorrin, Nicolas Kovensky, Martin Schvellinger, _Towards $1/N$ corrections to deep inelastic scattering from the gauge/gravity duality_, JHEP 04 (2016) 113 ([arXiv:1601.01627](https://arxiv.org/abs/1601.01627)) <a href="https://ncatlab.org/nlab/revision/diff/large+1%2FN+limit/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/4">v4</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

   added this pointer:

   • David Jorrin, Nicolas Kovensky, Martin Schvellinger, Towards $1/N$ corrections to deep inelastic scattering from the gauge/gravity duality, JHEP 04 (2016) 113 (arXiv:1601.01627)

   diff, v4, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeMar 11th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * Masayasu Harada, Shinya Matsuzaki, and Koichi Yamawaki, _Implications of holographic QCD in chiral perturbation theory with hidden local symmetry_, Phys. Rev. D 74, 076004 (2006) ([doi:10.1103/PhysRevD.74.076004](https://doi.org/10.1103/PhysRevD.74.076004)) <a href="https://ncatlab.org/nlab/revision/diff/large+1%2FN+limit/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/7">v7</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

   added pointer to

   • Masayasu Harada, Shinya Matsuzaki, and Koichi Yamawaki, Implications of holographic QCD in chiral perturbation theory with hidden local symmetry, Phys. Rev. D 74, 076004 (2006) (doi:10.1103/PhysRevD.74.076004)

   diff, v7, current

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2021
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to today's: * Yosuke Imamura, *Finite-$N$ superconformal index via the AdS/CFT correspondence* ([arXiv:2108.12090](https://arxiv.org/abs/2108.12090)) <a href="https://ncatlab.org/nlab/revision/diff/large+1%2FN+limit/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/10">v10</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

    added pointer to today’s:

    • Yosuke Imamura, Finite-$N$ superconformal index via the AdS/CFT correspondence (arXiv:2108.12090)

    diff, v10, current

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2023
    • (edited Jul 12th 2023)
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Edward Witten]], *Some Milestones in the Study of Confinement*, talk at *[Prospects in Theoretical Physics 2023: Understanding Confinement](https://www.ias.edu/video-tags/prospects-theoretical-physics-2023-understanding-confinement)*, IAS (2023) &lbrack;[web](https://www.ias.edu/video/some-milestones-study-confinement), [YT](https://youtu.be/TvIz-6YOdKs)&rbrack; with this quote: > [26:26](https://youtu.be/TvIz-6YOdKs?t=1586): "by now it's clear &lbrack;[Lucini & Teper 2001](large+N+limit#LuciniTeper01)&rbrack; that [[lattice gauge theory]], at least for the [[glueball]] sector, has made it clear that the [[large N limit|$1/N$-expansion]] is a good approximation to the real world, especially if you include a leading correction to the [[large N limit|large $N$ limit]]. Now unfortunately this is best established in the [[glueball]] sector, which is not very accessible experimentally." > [28:56](https://youtu.be/TvIz-6YOdKs?t=1736): "but the $1/N$ expansion doesn't explain everything. In fact, it's not hard to find phenomena in meson physics where the $1/N$-expansion does *not* work well." > [36:15](https://youtu.be/TvIz-6YOdKs?t=2175): "I suspect the [[large N limit|$1/N$-expansion]] works reasonably well for many aspects of [[baryons]]. However, as for mesons, it is easy to point to things that won't work well for baryons. In particular, among other things, I don't think the [[large N limit|$1/N$ expansion]] will be successful for [[nuclei]] as opposed to individual [[nucleons]]." > [37:12](https://youtu.be/TvIz-6YOdKs?t=2232): "I don' t think the phenomenological models used by nuclear physicists would have any success at of if the [[large N limit]] was a good description of [[nuclei]]." <a href="https://ncatlab.org/nlab/revision/diff/large+1%2FN+limit/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/11">v11</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

    added pointer to:

    • Edward Witten, Some Milestones in the Study of Confinement, talk at Prospects in Theoretical Physics 2023: Understanding Confinement, IAS (2023) [web, YT]

    with this quote:

    26:26: “by now it’s clear [Lucini & Teper 2001] that lattice gauge theory, at least for the glueball sector, has made it clear that the $1/N$-expansion is a good approximation to the real world, especially if you include a leading correction to the large $N$ limit. Now unfortunately this is best established in the glueball sector, which is not very accessible experimentally.”

    28:56: “but the $1/N$ expansion doesn’t explain everything. In fact, it’s not hard to find phenomena in meson physics where the $1/N$-expansion does not work well.”

    36:15: “I suspect the $1/N$-expansion works reasonably well for many aspects of baryons. However, as for mesons, it is easy to point to things that won’t work well for baryons. In particular, among other things, I don’t think the $1/N$ expansion will be successful for nuclei as opposed to individual nucleons.”

    37:12: “I don’ t think the phenomenological models used by nuclear physicists would have any success at of if the large N limit was a good description of nuclei.”

    diff, v11, current

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJul 1st 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * Kiril Hristov, *ABJM at finite $N$ via 4d supergravity*, J. High Energ. Phys. **2022** 190 (2022) &lbrack;[arXiv:2204.02992](https://arxiv.org/abs/2204.02992), <a href="https://doi.org/10.1007/JHEP10(2022)190">doi:10.1007/JHEP10(2022)190</a>&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/large+1%2FN+limit/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/large+1%2FN+limit/15">v15</a>, <a href="https://ncatlab.org/nlab/show/large+1%2FN+limit">current</a>

    added pointer to:

    • Kiril Hristov, ABJM at finite $N$ via 4d supergravity, J. High Energ. Phys. 2022 190 (2022) [arXiv:2204.02992, doi:10.1007/JHEP10(2022)190]

    diff, v15, current