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Could someone sketch me what algebraic geometry has to do with string theory? Are there other mathematical disciplines that are interwoven with string theory?

I'm aware of a similar question on math.stackexchange. But this doesn't answer my question.

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closed as too broad by John Rennie, Kyle Kanos, Brandon Enright, Prahar, Jim May 2 '14 at 14:23

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

This seems awfully broad. Can you pin down what you're trying to establish? For example, are you asking what you should read up on to start learning string theory? – John Rennie May 1 '14 at 7:52
I tried to look it up. The answer to first question may be: homological mirror symmetry, and the answer to the second question may be: symplectic geometry. I have no idea what either is (about). :) – Glen The Udderboat May 1 '14 at 11:36
Related: – Qmechanic May 1 '14 at 18:11

1 Answer 1

Algebraic geometry (along with almost any discipline of mathematics, even number theory) appears in many corners of string theory and other areas of physics, possibly too many to list.

E.g. typically the 6 compact dimensions of the 10-dimensional (super) string is taken to be a Calabi-Yau manifold, cf. e.g. this Phys.SE and links therein. Perhaps one of the more abundant sources of algebraic geometry is type IIA and type IIB string theories, which are interwoven by mirrorsymmetry.

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You could also add the statement that sheaves are used to represent D-branes in string theory, if I remember correctly. – Sanath Devalapurkar May 4 '14 at 16:27
@Sanath Devalapurkar: Good point. – Qmechanic May 4 '14 at 16:29

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