Can any other manifold be used for compactifying the 6 extra dimensions of string theory?

Question

I'm a layman interested in string theory. I read about how the 6 extra dimensions of superstring theory are compactified into 3-dimensional complex manifolds (so real dimension 6?) called Calabi-yau manifolds that have certain nice properties.

And I've read a little bit about the landscape too. So, we have a huge ($10^{500}$ to $10^{272,000}$) number of different Calabi-yau manifolds into which we can compactify the 6 extra dimensions, so string theory predicts every possible self-consistent theory of quantum gravity but the trouble is we need to choose the right Calabi-yau manifold which would result in the quantum gravity theory describing our universe. is that right?

My question is, can we compactify the extra dimensions into a different manifold? something other than Calabi-Yau manifolds, but you have much less number of different choices so that we can actually find the theory that describes our universe? is research being done on that? Also is it possible to compactify multiple different dimensions into multiple different manifolds? You have 6 extra dimensions right? Can you compactify 2 dimensions into a 1 dimensional complex manifold and the remaining 4 dimensions as a 4 dimensional real manifold? or something like that in order to reduce the number of choices?

Please don't use advanced math to answer it, I don't know any of the math yet.

Possible duplicates: Why (in relatively non-technical terms) are Calabi-Yau manifolds favored for compactified dimensions in string theory? and Could the 6 extra dimensions in superstring theory be a product of two manifolds? — Qmechanic, Apr 22 '22 at 19:43
@Qmechanic But it doesn't answer my question, why is my question closed? — mastershooter77, Apr 23 '22 at 06:34
Tip: An edit automatically makes the post enter the review queue for a second opinion. — Qmechanic, Apr 23 '22 at 07:38
A brief comment on the 2nd paragraph: There are not $10^{500}$ different CY-manifolds. Given some CY-manifold, the number of vacua (flux choices) can be like $10^{500}$ or even far more. The precise number of flux vacua depends on the choice of the CY. Btw. the $10^{272.000}$ arises from F-theory, where we compactify from 12D to 4D using a CY 4-fold. — psm, Apr 23 '22 at 09:03
@psm Oh I see, so what exactly are vacua\flux choices? are they what specify a theory of quantum gravity? — mastershooter77, Apr 23 '22 at 14:07
For instance, type IIB string theory contains higher dimensional versions of electric and magnetic fields (as strings and branes have higher dimensions). By changing the flux numbers, you can reshape the CY-manifold (without changing its topology!). So, for instance, you can increase the volume of the manifold, which may then lower the expected masses of certain particles. By playing around with those flux numbers, you can get different physical realities. Notice that the flux choice is not arbitrary, but limited. That's why we believe there's a finite number of vacua (physical realities). — psm, Apr 23 '22 at 14:57
@psm Oh wow can you do the opposite? Like if you know the mass of certain particles (which we do) can you find out the flux numbers? — mastershooter77, Apr 24 '22 at 02:44
Good question. It seems that this is generally extremely hard (maybe impossible), see e.g.: https://arxiv.org/abs/hep-th/0602072 — psm, Apr 24 '22 at 09:35
@Qmechanic The 2nd link you provided does answer my question, thank you. — mastershooter77, Apr 24 '22 at 10:01

Can any other manifold be used for compactifying the 6 extra dimensions of string theory?

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