Prerequisites for IAS volumes on Quantum Fields and Strings I'm a physics grad student interested in pursuing physics in a mathematically rigorous manner. However, I've hit a roadblock with the two volume book, Quantum Fields and Strings: A Course For Mathematicians by Deligne, et. Al.
I have covered enough Differential Geometry, Group Theory, Representation Theory and Functional Analysis to have a mathematically rigorous foundation in General Relativity and Non Relativistic Quantum Theory. It seems however that I require knowledge of considerably more to get through the aforementioned book.
Could someone with knowledge of the book's contents provide a detailed set of prerequisite topics in mathematics to help me cover it?
 A: The answer strongly depends on what you want to study; some sections are self-contained and others require prerequisites.
Examples:
No further background is required: The book has truly wonderful notes on supergeometry that are self-contained (assuming basic knowledge of differential geometry) for the one who wants to understand the geometry behind supersymmetry and supergravity. The parts on the foundations of quantum field theory are another good example of this category, you are ready for them if you have basic knowledge on quantum mechanics and functional analysis.
Some background is required: The notes on sigma-models and string theory of the second volume are marvelous, however, It would be very desirable to have complementary notes, because a lot has happened since the creation of the book that dramatically sharpened the clarity of the formal aspects and physics of the latter topics. A general suggestion could be to have at hand the following complementary resources: Notes On Super Riemann Surfaces And Their Moduli, Notes On Supermanifolds and Integration.
General suggestions:

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*The physical and mathematical preliminaries presented in the book "Mirror Symmetry (Clay Mathematics Monographs, Vol. 1)" are exactly the minimum (category theory, sheaf theory, algebraic geometry etc.) required to begin to work with the formal aspects of quantum fields and strings.


*I find Taubes book "Differential Geometry: Bundles, Connections, Metrics and Curvature (Oxford Graduate Texts in Mathematics, Vol. 23) 1st Edition" wonderful and well adapted to modern developments in gauge theory (specially in four dimensions)


*If you want to  begin to acquire detailed knowledge of complex algebraic geometry, I urge you to begin with the Shafarevich-Reid textbook "Basic Algebraic Geometry 1: Varieties in Projective Space". Simple, not much commutative algebra is required, and full of relevant examples.
If you have a particular inquietude or interest, tell us in the comments, surely someone would help in more precise grounds.
