Algebraic Geometry in String Theory?

Question

I'm currently studying String Theory and hope to do research in this area. I have now reached a point where even with a background in Mathematics instead of Physics, I have no clue what's going on mathematically.

So I've (re-)started reading up on more mathematics. This gave rise to the following question:

Is it "worth" studying Algebraic Geometry at this time? By "worth" it, I mean, will I benefit from this no matter what research direction in String Theory I will persue? Or is it rather specific?

(For clarification, "at this time" means I've worked my way through the book by Becker/Becker/Schwarz)

This post imported from StackExchange Mathematics at 2014-05-11 11:21 (UCT), posted by SE-user Mike

Comments

You should consider asking the same question on physics.stackexchange.com , as most people here are pure mathematicians.

This post imported from StackExchange Mathematics at 2014-05-11 11:21 (UCT), posted by SE-user Fredrik Meyer

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Michael: I just saw that you removed the previously added soft-question tag. That is fine. Just for your information: It is primarily intended for marking questions that don't admit a definite answer and are more of a subjective nature than of an objective (read: strictly mathematical) one. I don't think it was added in order to imply that your question is easy to answer or about easy and soft stuff. If you were surprised that someone else edited your question, see this part of the FAQ

This post imported from StackExchange Mathematics at 2014-05-11 11:21 (UCT), posted by SE-user t.b.

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Ahh I see, thanks for the heads up!

This post imported from StackExchange Mathematics at 2014-05-11 11:21 (UCT), posted by SE-user Mike

Answer 1

I only know about string theory from a (rather great) distance, and with the perspective of a pure mathematician who has colleagues in mathematical physics who think about the theory (some of whom were trained as physicists).

With this warning given, let me say that it seems to me that it would be near impossible to understand string theory without some understanding of algebraic geometry. I would adopt an analytic point of view, such as in the book by Griffiths and Harris (Principles of algebraic geometry), since this is going to be closer to the language that physicists use than a more algebraic treatment. You could also look at the books Quantum fields and strings: a course for mathematicians, by Deligne, Witten, et. al., which is based on a year long series of courses given at the IAS in 96-97, by Witten among others. I don't know how comprehensible these will be (since they are written from the point of view of leading those with rather strong mathematical training into some kind of understanding of the physics), but they may give an idea of what kind of geometry you should learn, and what kind of perspectives on that geometry would be useful.

This post imported from StackExchange Mathematics at 2014-05-11 11:21 (UCT), posted by SE-user Matt E