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nLab > Latest Changes: large N limit

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  1.  
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeApr 7th 2010

    We should have an entry on large N limit gradually. But sometimes it can be treated as a semiclassical limit. I quoted a reference by Yaffe where I originally read of that approach to the entry semiclassical expansion.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2020
    • (edited Jan 5th 2020)

    added references on ’t Hooft double line notation for gauge group SO(N)SO(N) and unoriented worldsheets

    (I see that Predag Cvitanovic says in his Birdtracks book that he has something on this, but I haven’t extracted that yet.)

    diff, v10, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 6th 2020

    He seems (p. 42) to be referring to Fig. 16 of this. Presumably he absorbed this into his Birdtracks notation.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 6th 2020

    That’s it, Thanks!!

    I’ll be starting a dedicated entry ’t Hooft double line construction…

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 6th 2020

    On the ’Literature’ tab of his site, he says that paper is superseded by his book,

    but contains interesting material (counting of invariants, graphs, etc.,) not included in the webbook.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 6th 2020

    Thanks. Do you see where in the book this is? (BTW, finally found the pdf…)

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 6th 2020

    Is that (9.57)?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 6th 2020

    Thanks! Yes, that’s at least the case of 𝔰𝔲(N)\mathfrak{su}(N).

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 6th 2020

    Presumably the notation in (10.13) and (12.9) is giving those results for SO(n)SO(n) and Sp(n)Sp(n).

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJan 6th 2020

    Thanks again! Have now added this here.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 6th 2020

    I have re-written and considerably expanded the Idea-section.

    Also expanded and (re-)organized the list of references.

    diff, v12, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJan 30th 2020

    added pointer to today’s

    • Margarita Garcia Perez, Prospects for large NN gauge theories on the lattice (arXiv:2001.10859)

    diff, v25, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2020

    added these early references:

    • A. Gonzalez-Arroyo, M. Okawa, A twisted model for large NN lattice gauge theory, Physics Letters B Volume 120, Issues 1–3, 6 January 1983, Pages 174-178 (doi:10.1016/0370-2693(83)90647-0)

    • A. Gonzalez-Arroyo, M. Okawa, Twisted-Eguchi-Kawai model: A reduced model for large- NN lattice gauge theory, Phys. Rev. D 27, 2397 (1983) (doi:10.1103/PhysRevD.27.2397)

    diff, v28, current

    • CommentRowNumber14.
    • CommentAuthorzskoda
    • CommentTimeMar 1st 2023
    • Grégory Ginot, Owen Gwilliam, Alastair Hamilton, Mahmoud Zeinalian, Large N phenomena and quantization of the Loday-Quillen-Tsygan theorem, Adv. Math. 409A (2022) 108631

    diff, v31, current

    • CommentRowNumber15.
    • CommentAuthorzskoda
    • CommentTimeMar 16th 2023
    • (edited Mar 16th 2023)

    Publication data for

    • Semyon Klevtsov, Random normal matrices, Bergman kernel and projective embeddings, J. High Energ. Phys. 2014, 133 (2014) doi arXiv:1309.7333

    and reference

    related to the earlier reference

    diff, v33, current

    • CommentRowNumber16.
    • CommentAuthorzskoda
    • CommentTimeMar 16th 2023

    Application of WKB method:

    • V. P. Maslov, O. Yu. Shvedov, Large-N expansion as a semiclassical approximation to the third-quantized theory, Physical Review D60(10) 105012 doi

    diff, v33, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2023

    added pointer to:

    diff, v35, current

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2023

    added pointer to today’s

    diff, v36, current

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeDec 28th 2023
    • (edited Dec 28th 2023)

    added pointer to yesterday’s

    • Jan Albert, Johan Henriksson, Leonardo Rastelli, Alessandro Vichi, Bootstrapping mesons at large NN: Regge trajectory from spin-two maximization [arXiv:2312.15013]

    diff, v37, current

    • CommentRowNumber20.
    • CommentAuthorUrs
    • CommentTimeJan 18th 2024

    added pointer to today’s

    • Marco Bochicchio, Mauro Papinutto, Francesco Scardino, On the structure of the large-NN expansion in SU(N)SU(N) Yang-Mills theory [arXiv:2401.09312]

    diff, v38, current

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