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It can be assumed I have taken introductory courses of GR (Carroll) and QFT(Schwartz).

I skimmed through this book by Marcolli on Seiberg-Witten (SW) gauge theory. What I have understood after looking at it is: I will be needing Algebraic topology. Also, after looking into few supersymmetry lecture notes on arXiv I found that SW gauge theory is also introduced there as well under the section/chapter of $S$ or $T$ duality. Of course, I can pick a book on Algebraic Topology to get familiarity with the meaning of terms used in the book of Marcolli. BTW will I be needing any other mathematical pre-requisites (ex. Algebraic Geometry)?

But what I had in mind is book or lecture notes which does SW theory from ground up regarding mathematical pre-requisite like how it's usually done in GR books (not going through a whole differential geometry math book) or how the group theory is tackled in Schwartz book.

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    $\begingroup$ At this level you are getting into cutting edge research where a lot of knowledge is not recorded in a book. It's possible someone will know of a book, but I would say your best bet is to go to the original papers on this subject, and chase down any references they give for the parts you are not comfortable with. Also I would suggest you don't try to read an entire textbook on Algebraic Topology, but rather identify the specific pieces that you need for your interests and focus on those. $\endgroup$
    – Andrew
    Nov 15, 2020 at 14:23

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First, Marcolli's book is an extremely mathematical to the subject, many other excellent and much more physical introductions are available. Indeed, the original paper is very readable and use very little algebraic topology.

If you are motivated enough to read at the level of mathematical rigor of Marcolli's book, I suggest to use the excellent, introductory and self-contained Nicolaescu's notes on Seiberg-Witten theory as a parallel reading and Cecotti textbook "Supersymmetric Field Theories" for useful introductions to the required (complex and Kahler) geometry.

If you are familiar with the basics of string theory, you may try Introduction to Seiberg-Witten Theory and its Stringy Origin.

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