TITLE: String Theory: What to do?
QUESTION [78 upvotes]: This is going to be a relatively broad/open-ended question, so I apologize before hand if it is the wrong place to ask this.
Anyways, I'm currently a 3rd year undergraduate starting to more seriously research possible grad schools.  I find myself in somewhat of a weird spot as my primary interests lie in physics, but I usually can't stand the imprecision with which most physicists do physics.  I eventually would like to do work relevant to the quest of finding a theory of everything, but because I do not like the lack of rigor in physics, I have decided not to go to graduate school in physics.  However, when looking at the research interests of faculty members, I've found that most institutions have zero, one, or occasionally two (mathematics) faculty members working in this area.  Am I just not looking in the right places?  Where I am to go if I am looking to get into a field like String Theory from a mathematician's perspective?
As a separate but related question, I've found the prerequites for string theory to be quite daunting.  At this point, I feel as if it will be at least another year or two before I can even start learning the fundamentals of the theory (I won't even be taking a course in QFT until next year).  To be honest, I am starting to feel a little scared that I won't have enough time to do my thesis work in a field related to string theory.  Compared to algebraic topology or something, which I took last year, this year and next I could be learning more advanced aspects of the field so that by the time I got to grad school I could immediately jump in and start tackling a problem, whereas with string theory I feel as if I won't be able to really do this until my third year of grad school or so.  Is this something I should actually be worried about, or am I worrying about nothing?
Also, if any of you have studied string theory, I would be interested in knowing what subjects I should study to prepare myself and textboks that you recommend for studying from.  I would prefer textbooks about physics written by a mathematician or at least a great deal of mathematical rigor, although I am willling to compromise.
Thanks before hand for all the help/suggestions.  I am interested to hear mathematicians' take on this.
EDIT:  A comment made me think that I should point out that I am ultimately interested in a theory of everything, not string theory per se.  At this point, because I have so much to learn, I think that if I head in the direction of string theory (learn things like QFT, GR, Conformal Field Theory, Supersymmetry, etc.) I can't go wrong.  It won't be for awhile until I have to really make a choice between candidates for a TOE.

REPLY [10 votes]: There are two ways to proceed as a pure mathematician: You can specialize in differential geometry and become an expert in general relativity: This is a theory that is mathematically rigorous, and a challenge.
You could also specialize in operator algebras, which is a huge and very active topic. There is an axiomatic, mathematically rigorous approach to quantum field theory, called axiomatic, local or algebraic quantum field theory, that uses and needs a lot of material from operator algebras. The cooperation of physicists and mathematicians has been rich and fruitful, much like in general relativity.
Have a look at AQFT in the nLab.
A good start is the classic book

Bogolyubov, Logunov, Oksak, Todorov: General principles of quantum field theory (Mathematical Physics and Applied Mathematics, 10. Dordrecht etc.: Kluwer Academic Publishers, 1990)

In both cases you'll have the opportunity to pursue an academic career in a math department, while continuing your quest to better understand the fundamental problem of a TOE.
Edit and Addendum: As you can read in the comments to other answers, there currently is no rigorous construction of an interacting field theory in 4D in local/algebraic/axiomatic QFT, which is the reason why most theoretical physicists don't actively pursue this approach anymore. But some do, it is certainly worth knowing the many nontrivial deep model independent results, and the leading string theorists know a lot about this approach, too. (And yes, Witten has also (co-)written papers about it.)
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