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## Summary:

- Alternatives to Calabi Yau?

## Main Question or Discussion Point

Are there alternatives to Calabi Yau spaces describing dimensions in superstring theory? If yes, what are they? If no, why?

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- Thread starter StenEdeback
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- #1

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## Summary:

- Alternatives to Calabi Yau?

Are there alternatives to Calabi Yau spaces describing dimensions in superstring theory? If yes, what are they? If no, why?

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Moderator's note: Moved thread to the Beyond the Standard Model forum.

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Yes, D-brane worlds.

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Thank you, Demystifier!

Sten E

Sten E

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haushofer

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You mean by "describing dimensions" "compactifications to 4 spacetime dimensions?"

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Yes, that is a good way of putting it. I wonder if Calabi Yau are the only players in that game, or if there are other ways of handling all these extra dimensions.

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As for compactification, there are also orbifolds.

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samalkhaiat

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Calabi-YauAs for compactification, there are also orbifolds.

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Thank you Demystifier and samalkhaiat! I will have a look at orbifolds.

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Yes. But some orbifolds are not manifolds, and obviously I meant those orbifolds.Calabi-Yauisan orbifold.

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samalkhaiat

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Yes, they seem so. Broadly speaking, compactification requires Ricci-flat compact (complex) space. Ricci-flatness and compactness are what CY spaces have. Of course, finding the right one is another story.I wonder if Calabi Yau are the only players in that game,

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Why does compactification requires Ricci flatness? Does it depend on a requirement that some supersymmetry survives at low energies, or is there an argument that does not depend on supersymmetry?compactification requires Ricci-flat

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samalkhaiat

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Consider [itex]M^{D} = M^{d} \times K^{D-d}[/itex]. From Supergravity action you obtain the Einstein equation in [itex]M^{D}[/itex]: [tex]R^{(D)}_{AB} = 0.[/tex] This implies, [tex]R^{(d)}_{\mu\nu} = 0, \ \mbox{&} \ R^{(D-k)}_{mn} = 0.[/tex]Why does compactification requires Ricci flatness?

I would agree with that, if I was a phenomenologist. Mathematically, world-sheet supersymmetry means that there are Killing spinors, [itex]\nabla \epsilon = 0[/itex], on the target space of the critical dimension [itex]M^{10}[/itex]. Then, one can easily show that [itex]\nabla \epsilon = 0 \ \Rightarrow \ R^{(10)}_{AB} = 0[/itex]. So, if you consider the solution [itex]M^{10} = M^{4} \times K^{6}[/itex], then [itex]\mbox{Ric}(K) = 0[/itex].Does it depend on a requirement that some supersymmetry survives at low energies,

You can't avoid supersymmetry in superstrings. Where do the fermions come from?is there an argument that does not depend on supersymmetry?

- #14

MathematicalPhysicist

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An interesting book on my endless book list is:Thank you Demystifier and samalkhaiat! I will have a look at orbifolds.

https://www.amazon.com/dp/0521870046/?tag=pfamazon01-20&tag=pfamazon01-20

Seems like a good starting place, but other than that I don't know since I haven't even started reading this book, I have other books on my reading right now.

Cheers!

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Well, at least for academic purposes one can study compactification in 26-dimensional bosonic string theory. By replacing supergravity action with bosonic field action, your argument can be used to argue that we would need Calabi-Yau even then, am I right?You can't avoid supersymmetry in superstrings. Where do the fermions come from?

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samalkhaiat

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No. In order for the compact internal space [itex]K^{D-4}[/itex] to be a CY space, itWell, at least for academic purposes one can study compactification in 26-dimensional bosonic string theory. By replacing supergravity action with bosonic field action, your argument can be used to argue that we would need Calabi-Yau even then, am I right?

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