I was searching for introductions to current mathematics related to gauge theories.

Can someone suggest some good references?


Topics in Physical Mathematics by K. Marathe

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    $\begingroup$ 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. $\endgroup$ Commented Nov 25, 2011 at 14:18
  • $\begingroup$ 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. $\endgroup$ Commented Nov 25, 2011 at 14:28
  • $\begingroup$ (ie. current pure mathematics inspired by / from "gauge (field) theory" in physics) $\endgroup$ Commented Nov 25, 2011 at 14:30
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    $\begingroup$ This question is awfully broad. Are you looking for introductions to areas like Donaldson theory or Seiberg-Witten theory? $\endgroup$
    – S. Carnahan
    Commented Nov 26, 2011 at 3:48

2 Answers 2


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

Gauge Fields: An Introduction To Quantum Theory


Kevin Costello, Renormalization and Effective Field Theory

Frédéric Paugam, Towards the mathematics of quantum field theory


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