All Questions
5 questions
6
votes
2
answers
565
views
Why do you need to count curves on Calabi-Yau manifolds in string theory?
One of the mathematical fields that string theory is said to have had a large bearing on is enumerative geometry which, roughly, deals with counting rational curves on hypersurfaces and its ...
- 8,642
-2
votes
1
answer
157
views
How Quintic 3-fold is a Calabi–Yau manifold and has non-vanishing Ricci scalar?
It’s well known that quintic 3-fold is a Calabi-Yau manifold in the complex projective space $\mathbb{CP}^{n+1}$ , see for instance:
https://en.wikipedia.org/wiki/Quintic_threefold
Now the main ...
- 463
2
votes
0
answers
196
views
In what sense are solutions to the Dirac equation and solutions to the Laplace equation equivalent in string theory?
I have come across statements like elementary particles on a Calabi-Yau correspond to harmonic forms (or to cohomology classes, which is equivalent for a compact Kähler manifold, since every ...
- 9,454
7
votes
1
answer
695
views
Determining the Hodge numbers of some orbifold examples
I'm currently reading about complex geometry in order to get a feeling of how to determine the Hodge numbers, e.g. of certain orbifold constructions. Since I'm a physicist with no deeper mathematical ...
- 909
8
votes
3
answers
406
views
Does the complex 3-sphere have a complex structure modulus?
This question has a flavor which is more mathematical than physical, however it is about a mathematical physics article and I suspect my misunderstanding occurs because the precise mathematical ...
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