I know that we can use the SU($n$) 6d (2,0) SCFT, the M5-brane world-volume theory to get $\mathcal{N}=2$ theories. Still, e.g. reading Tachikawa's "Supersymmetric dynamics for pedestrians" I cannot understand how one gets the SW curve for say pure $\mathcal{N}=2$ or the theory with $N_f=1,2,3,4$. Although I kind of understand how to obtain the BPS particles' charges the main part of my question is still a mystery to me. So to repeat:

What is exactly the exact mechanism of M-theory (and M5-branes) that gives the (pure for simplicity) $\mathcal{N}=2$ SW curve $y^2=(x-u)(x-\Lambda)(x+\Lambda)$?

If you don't know the answer, do you know a reference that explicitly describes this point? Of course Witten's paper 9703166 provides a lot of details, but I am mostly looking for the general "spirit" of the solution rather than technical details.


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