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Which is the role of Algebraic Geometry in String Theory?

+ 5 like - 0 dislike
2841 views

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. But this doesn't answer my question.
This post imported from StackExchange Physics at 2014-05-04 11:20 (UCT), posted by SE-user Anne O'Nyme

asked May 1, 2014 in Mathematics by Anne O'Nyme (170 points) [ revision history ]
recategorized May 11, 2014 by dimension10
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?

This post imported from StackExchange Physics at 2014-05-04 11:20 (UCT), posted by SE-user John Rennie
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). :)

This post imported from StackExchange Physics at 2014-05-04 11:20 (UCT), posted by SE-user Glen The Udderboat
Related: physics.stackexchange.com/q/2528/2451

This post imported from StackExchange Physics at 2014-05-04 11:20 (UCT), posted by SE-user Qmechanic

1 Answer

+ 3 like - 0 dislike

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.

This post imported from StackExchange Physics at 2014-05-04 11:20 (UCT), posted by SE-user Qmechanic
answered May 1, 2014 by Qmechanic (2,790 points) [ no revision ]

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