Studying Mathematics to Understand String Theory/SuperString

[wyattbohr]

I just recently graduated with a mathematics degree. Lately, I've been very fascinated with quantum mechains and string theory, but when I try to do research I am a little overwhelmed by all the varying topics of advanced mathematics I have to know. Can anyone suggest mathematical topics to teach myself to better understand string theory and quantum mechanics? Thank you :)

 

[fresh_42]

I just recently graduated with a mathematics degree. Lately, I've been very fascinated with quantum mechains and string theory, but when I try to do research I am a little overwhelmed by all the varying topics of advanced mathematics I have to know. Can anyone suggest mathematical topics to teach myself to better understand string theory and quantum mechanics? Thank you :)

I would say: functional analysis, Lie theory and a bit abstract algebra of graded Lie algebras.

From a mathematical point of view, I have a book about "Supermanifolds and Virasoro Algebras", unfortunately I don't know whether an English version exists.

 

[mathwonk]

I don't know string theory, but I was once an invited speaker at a conference for people who wanted to learn my subject for use in string theory. I got the impression that Riemann surfaces is a key topic in that area. Indeed "strings" are apparently essentially Riemann surfaces. Here is a reference to the proceedings of that conference, which are somewhat scarce, but may be in libraries.
(I gave away my own copy when I moved.

https://www.amazon.com/dp/9971509032/?tag=pfamazon01-20

 

[haushofer]

The book I used for this is Nakahara:

https://www.amazon.com/dp/0750306068/?tag=pfamazon01-20

This is in my experience the best book to look for; it also contains some topics on QM. But the basis for doing string theory is Quantum Field Theory and General Relativity (and all the accompanying math). If you don't master these topics, string theory is way out of your league.

To get an idea, the most approachable book on string theory is Zwiebach. But also be aware that it's very thorough about a lot of stuff which is skipped by more advanced texts. Topics like conformal field theory or supersymmetry are not or barely touched.