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I am reading Verbaarschot's course notes on Topics in random matrix theory, seeing many computations being done but not what the purpose of all these computations is. I wonder about the global picture of what is going on and why this is done, and what is the physical meaning of what is calculated. I'd like to have a sort of bird's eye view, describing informally what one can hope to compute and/or understand about QCD by working with random matrices, and the kind of results and or insights one can achieve - thus adding intuitive meaning to the formal development.
This is quite thoroughly discussed in this review: Random Matrix Theory and Chiral Symmetry in QCD by Verbaarschot and Wettig.
The gist is that in the deep infrared, the chiral random matrix model belongs to the same universality class as QCD does, so one can hope to obtain all the universal results of infrared QCD. The review mentions one such application is the derivation/reproduction of Leutwyler-Smilga sum rules.
My lack of background on random matrix theory prevents me from reading far into that review, I hope I can add more in the future.
I am particularly interested in how the techniques compare with those based on the Skyrme model.
Do you now have deeper insights into this? I am still interested!
@Arnold, not yet, but I just started seriously learning disordered/matrix models recently, ask me later! But don't feel bad if you can't understand the review, one of the author himself acknowledges the article is not pedagogical enough due to page limitation imposed the by publisher.
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