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The question I guess is pretty clear. I am a physics undergrad wishing to pursue research in quantum gravity(string theory?). What are the subjects I should learn other than the usual compulsory undergrad courses such as quantum mechanics, and GR, etc? Things that come to my mind are QFT, lie algebras, differential geometry, algebraic geometry etc? Other than this, could you suggest any topic that are not entirely essential but interesting in mathematical physics, gauge theory etc (e.g. solitons, monopoles etc). Actually I am looking for a mini project of sorts which would give me an idea of what these fields really are. I have done some lie algebras, classical field theory and am currently studying QM.

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up vote 2 down vote accepted

First, be proficient in QFT and GR. And by this, not just 'undergrad' versions, but with mathematical rigor -- that includes being fluent in differential geometry and gauge theory. Depending on what type of string theory work you do, and a response to your request of "not entirely essential but interesting", would be to know Algebraic Topology (in order to make sense of TQFT). At this point, you're becoming more of a mathematician -- this is no surprise, it is in essence a mathematical topic. Take a look at Nakahara's textbook "Geometry, Topology, and Physics" for a start (before you begin to think about String Theory).

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Nice answer. I have done done bits of Nakahara and Naber. Which parts of the book do you think are important? –  ramanujan_dirac Sep 5 '12 at 21:53
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I have to second this. Learn GR inside and out, and not even because you want to be a string theorist, but because it's beautiful. Also, I don't know why GR isn't a standard undergraduate topic, but "graduate" GR as I've seen it taught is something a motivated undergrad could master in a few weeks. –  wsc Sep 5 '12 at 22:20
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The point is to just envelop yourself with this mathematical way of thinking. At some point all of this math will become relevant. You will tweak your needs when you start reading papers and seeing gaps in your understanding. –  Chris Gerig Sep 6 '12 at 1:02
    
how much mathematics should one know to study string theory @ChrisGerig –  Arafat Oct 12 '13 at 16:41
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From a practical perspective, when it comes to competing with other students for a spot in the string theory group, there are heavy parameters being weighed other than "what you know". You must have research experience, at least 3 years of it; to get into graduate school (for any field), period. Also understand that counselors hear "I want to go into string theory" from 3 out 4 entering graduate students in their physics department. Also, understand that a job in industry is hard enough to find with an experimental physics background, much less resume featuring a cryptic frontier theory. Depending on you conviction for string theory, I encourage you to have a fallback field of study, because chances are you will be put there by the counselor due to the limited space of the theory group.

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What do you mean by a fallback study of field. Do you mean I should study something else too and not only string theory related things? or should I apply to non-string theory positions for my PhD in addition to string theory. I dont know much about PhD applications, but I thought we have to specify only 1 field. BTW, I didnt -1 you. I didnt know, y it was downvoted. –  ramanujan_dirac Sep 5 '12 at 16:24
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What graduate school did you attend that required at least three years of research and 3/4 of the students wanted to go into string theory? That doesn't sound like any program I'm familiar with. In fact the most competitive groups where I am are pretty high-profile CME labs. –  wsc Sep 5 '12 at 22:11
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Physics departments have their research professors decide on candidates primarily on their field of interest, i.e. experimental vs theory, and fields such as solid-state, optics, nuclear, gravitational, string theory, etc. Professors need to fill their labs, and groups like string theory get filled the fastest. A candidate interested in condensed matter physics (experimental) is more like to get accepted into the program, compared to a string theory candidate. If you have already accepted the PhD offer, they will most like try to recruit to into a different group other than string theory. I did experimental physics research for a number of years, and that was the predominant factor that got me accepted into a graduate program.

My post above was probably down-voted because it is skeptical, doesn't directly address the original question; but it is important advice for a candidate in my humble opinion.

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