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? I'm also open to suggestions of other texts that may be more suited to a physicist, while still being mathematically rigorous.