This question was asked on Theoretical Physics Stackexchange and was grossly mis

Question

This question was asked on Theoretical Physics Stackexchange and was grossly misread and closed. I am again posting the question here hoping to get some valuable insights.

Also some people were unhappy with the term Maldacena conjecture since there is so much evidence in favour of "AdS/CFT". I guess still the point remains that there is no true "proof". Isn't it true that the Gopakumar-Vafa invariants were discovered in an attempt to "prove" AdS/CFT?

To put one of the central questions first - I guess the canonical resource to learn about Maldacena's conjecture is the famous "MAGOO" review or may be the Hoker and Freedman's review. Any other suggestions? The "problem" I see is that standard QFT courses don't teach about N=4 SYM or about N=8 Supergravity and absolute fluency with such stuff seems to be utterly necessary for getting into this field. How does one develop this and from where and how much time should it require?

Most bizarrely someone read this question as being asking as to what is the "least" one can study and "become" another Jacob Bourjaily! (whatever that means!) Thats farthest from the intention. There is no denying of the fact that some people have intrinsic IQ edges over others but that is hopefully not a reason for others to stop trying to be the best! (..I am being hopelessly optimistic that non-exceptional people also can produce cutting edge string theory results!..) On the contrary the point of this question is to want to know as to at what rate do the best students work and study. Its more like wanting to know what do speeds of study of "most of the best" students look like.

Surely there is not one-size-fits-all answer to this but surely there are generic patterns to how the cutting edge string and field theorists of today did their graduate school. As to what courses did they take at what stage and how much of what they learn by when and from where.

I would like to know as to how or at what rate does the academic life or a good graduate student progress in a theoretical physics grad school if he/she is aiming to specialize in topics like say the Maldacena conjecture (or "AdS/CFT" as it is often said), or issues of integrability emerging from it and such related questions. I have in my mind "role models" of certain brilliant students who have recently completed their PhDs in such stuff like Jacob Bourjaily, Tudor Dimofte, Silviu Pufu etc.

Assume that a grad student starts learning QFT and related mathematics from the first day of grad school (which I guess is already too late!) I guess some of these recent very successful PhDs were way ahead of such scenarios!

Then, how much and how far into QFT should someone know before he/she can get into cutting edge of Maldacena's conjecture?

To split up the question,

How long should it take to learn enough of QFT (what is enough?) ?

At what stage and after knowing how much of QFT should one be able to start learning String Theory?

How long and how much of String Theory should one know before being able to get through the literature in the topics mentioned above?

Can one start reading the papers (or even working?) in these topics along with learning QFT?

Can one start learning String Theory along with learning QFT or do they have to come in a strict order?

For all of these above questions I would love to know of the characteristic time-line in terms of months into graduate school when each of these milestones should be covered.

I guess this will help know what is the right pace to work at - which I guess was the speed in which some of these people mentioned earlier worked at.

Explanation / Answer

The problem is not any "intrinsic IQ edges". These are mythological things that do not affect research results. As Mark Twain said, it ain't the things that we don't know, but the things we know that just ain't so. Courses teach you things that just ain't so.

The time spent asking questions about how to learn XYZ is better spent asking questions about XYZ. The way to do this is to consider a specific physical problem, and solve it. If you can't solve it, read some papers, and then solve it.

Nothing about AdS/CFT is taught in graduate school. The reason is structural--- there are always many more people who are interested in strings than there are who are interested in spintronics. So the graduate courses are structurally designed to push people out of string theory and towards something practical. The timeline for learning any amount of string theory in school is therefore ?-months.

To learn AdS/CFT, read the original papers. They are very accessible if you have the string theory background. It is not good enough to read the reviews, even the best ones, you should learn the brane constructions of the 90s, because these contain an enormous amount of black hole physics. BFSS matrix theory is essential too, because this is a simpler arena pre-AdS/CFT, which forshadowed it, and I personally find the physics of BFSS more monstrously counterintuitive, although it is just a version of AdS/CFT. It is somehow more difficult to see 10 dimensions emerging than 1 plus a sphere.

Learning field theory today is not hard--- you can do it relatively quickly from some Wilsonian reviews. Field theory is useful outside of high-energy physics, and so is sometimes taught properly. Learning perturbation theory can take 1 day, or it can take 10 years, depending on whether you learn the path integral first. Lean the path integral first. Ignore anything Dysonish that does Wick's theorem by normal ordering time-ordered operators, and if someone is doing this, they are incompetent, and you can ignore all their research papers too. Dyson's methods were a stopgap measure to get physicists in the 1950s who refused to learn path-integrals to learn Feynman diagrams.

The central barrier is learning string theory, and to do this, one must read the original papers on dual resonance models, especially Veneziano's nice review of the early 1970s, and Mandelstam's. These are not accessible nowadays, because they require familiarity with S-matrix theory and Regge theory, neither of which exist as disciplines anymore. This is a terrible shame, but you can fix that by reading up books and articles from the late 1960s on your own. There is no way to understand string theory without going through Regge theory, which is why all the good string theorists are old. They protect their monopoly on knowledge by hiding Regge theory and S-matrix theory from the younger folks, although I am sure they do not do so consciously, only structurally.

The original papers on N=8 SUGRA used computer algebra to find the Lagrangian. The supergravity Lagrangian is so complicated, it is hard to use, certainly you can't use it for perturbative calculations because they are just too complicated in any formalism. The modern methods for calculating N=8 SUGRA amplitudes work them out using analyticity and unitarity from tree scattering, which is determined by symmetry. This is a revival of S-matrix theory, as applied to field theory, and it is a welcome breath of fresh air, after 40 years of heckling and suppression.

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