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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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.

  • $\begingroup$ You could also add the statement that sheaves are used to represent D-branes in string theory, if I remember correctly. $\endgroup$ – user28355 May 4 '14 at 16:27
  • $\begingroup$ @Sanath Devalapurkar: Good point. $\endgroup$ – Qmechanic May 4 '14 at 16:29

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