11
$\begingroup$

I was hoping for an answer in general terms avoiding things like holonomy, Chern classes, Kahler manifolds, fibre bundles and terms of similar ilk. Simply, what are the compelling reasons for restricting the landscape to admittedly bizarre Calabi-Yau manifolds? I have Yau's semi-popular book but haven't read it yet, nor, obviously, String Theory Demystified :)

Improve this question
$\endgroup$
1

3 Answers 3

Reset to default
6
$\begingroup$

There is one simple reason: in such scenario the physics at the string scale has supersymmetry. Supersymmetry (more technically $N=1$ supersymmetry) has some nice phenomenological features that make it an attractive bridge between low energy physics and string theory. The existence of this symmetry translates directly to the requirement that the compactification manifold is Calabi-Yau.

Improve this answer
$\endgroup$
0
2
$\begingroup$

Since the word "supersymmetry" did not appear in your list of forbidden words let me give you this answer:

Because Calabi-Yau manifolds leave unbroken some part of the original supersymmetry, which is advantageous for model building.

But there are alternatives to Calabi-Yaus, like flux compactififcations or large extra dimensions.

Improve this answer
$\endgroup$
2
  • $\begingroup$ how can large extra dimensions be consistent with everyday experience? $\endgroup$
    – lurscher
    Commented Feb 11, 2011 at 16:20
  • 4
    $\begingroup$ "Large" means "much larger than the Planck scale", but it still can be tiny. Interestingly, experiments do not rule out large extra dimensions of sub-millimeter size. See, for instance, arxiv.org/abs/hep-ph/0011014 $\endgroup$
    – Daniel Grumiller
    Commented Feb 11, 2011 at 19:01
2
$\begingroup$

We can have compactifications over 7D manifolds with a $G_2$ holonomy, or an 8D manifold with an $SO(7)$ holonomy. We can have orbifolds, or flux compactifications. We can have warped compactifications like $AdS_5 \times S^5$.

Improve this answer
$\endgroup$
1
  • $\begingroup$ But, what is the physical reason why we are required to have a $G_2$ holonomy? I understand the reasons for requiring any compaction, but not specifically one with Ricci zero curvature, which is what leads to Calabi-Yau manifold. $\endgroup$
    – Davius
    Commented Sep 15, 2022 at 17:42

Not the answer you're looking for? Browse other questions tagged or ask your own question.