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Mitchell Porter
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Sati and Schreiber claim that their hypothesis on the "cohomotopic" foundations of M-theory, implies the ad-hoc rules of Hanany-Witten theory. See section 4.10 of "Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams".

Maybe their work is a little too modern for your purposes :-) ... but you still might want to see what they say on this topic. Their most recent reference on Hanany-Witten is a 2017 thesis, which at least is a lot more recent that Giveon and Kutasov.

As for Seiberg dualities via Hanany-Witten, Adi Armoni has written a few papers applying them that I found interesting. They aren't reviews, but you could still have a look.

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