I was searching for introductions to current mathematics related to gauge theories.
Can someone suggest some good references?
E.g.
Topics in Physical Mathematics by K. Marathe
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1$\begingroup$ Since you are asking for "mathematics related to gauge theories" I am assuming that you mean "gauge theory" in the context of physics. In mathematics, the term "gauge theory" is a well-defined subfield of differential geometry: the study of connections on vector bundles, usually with special properties, and their associated moduli spaces. This is a huge area of current mathematical research. Some of it is physics inspired, but certainly not all of it. $\endgroup$– Spiro KarigiannisNov 25, 2011 at 14:18
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$\begingroup$ If I'm not mistaken "gauge field" in physics is equivalent to "connections on vector bundles" in maths. - In the context of your comment, I mean 'gauge theory' in the context of maths. $\endgroup$– Sadiq AhmedNov 25, 2011 at 14:28
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$\begingroup$ (ie. current pure mathematics inspired by / from "gauge (field) theory" in physics) $\endgroup$– Sadiq AhmedNov 25, 2011 at 14:30
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1$\begingroup$ This question is awfully broad. Are you looking for introductions to areas like Donaldson theory or Seiberg-Witten theory? $\endgroup$– S. Carnahan ♦Nov 26, 2011 at 3:48
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2 Answers
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See these
Quantum Fields and Strings: A Course for Mathematicians
Quantum Field Theory for Mathematicians
and, as a physicist, I would also add Faddeev and Slavnov
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Kevin Costello, Renormalization and Effective Field Theory
Frédéric Paugam, Towards the mathematics of quantum field theory
answered Nov 25, 2011 at 17:55