2
votes
1answer
80 views

Calabi-Yau condition, moduli and Lichnerowicz equation

I have a conceptual confusion about the metric moduli of Calabi-Yau manifolds, when I was reading Calabi-Yau compactification. As I understand, the metric moduli is parametrized by infinitesimal ...
3
votes
1answer
65 views

What is the need to consider a singular spacetime?

To have a consistent superstring theory (which is to avoid the conformal anomaly on the worldsheet CFT) we are forced to build our theory on the critical dimension $n=10$. However, the Standard ...
5
votes
1answer
97 views

Fundamental group of Calabi-Yau 3-fold in string theory

In string theory, we compactify a 10-dimensional space by a Calabi-Yau 3-fold to reduce the dimension to 4. To get a reasonable theory, a Calabi-Yau 3-fold should satisfy some properties. One is the ...
6
votes
2answers
191 views

What happens if the holonomy group lies in $SU(2)$ for a CY 3-fold?

I am a mathematician and reading a physics paper about the holonomy group of Calabi-Yau 3-folds. In that paper, a Calabi-Yau 3-fold $X$ is defined as a compact 3-dimensional complex manifold with ...
6
votes
1answer
191 views

How exactly are Calabi-Yau compactifications done?

To compactify 2 open dimensions to a torus, the method of identification written down for this example as $$ (x,y) \sim (x+2\pi R,y) $$ $$ (x,y) \sim (x, y+2\pi R) $$ can be applied. What are the ...
1
vote
1answer
217 views

Calabi-Yau manifolds and compactification of extra dimensions in M-theory

I just finished learning M(atrix) theory and the basics of the compactification of extra dimensions. The extra 6 dimensions of superstring theory can be compactified on 3 Calabi-Yau manifolds ...
5
votes
0answers
103 views

Calabi Yau compactification based on U(1) charges

In Green-Schwarz-Witten Volume 2, chapter 15, it is argued (roughly) that we need 6-dimensional manifolds of $SU(3)$ holonomy in order to receive 1 covariantly constant spinor field. And it turns out ...
5
votes
1answer
371 views

CY moduli fields

When one does string compactification on a Calabi-Yau 3-fold. The parameters in Kähler moduli and complex moduli gives the scalar fields in 4-dimensions. It is claimed that the Kähler potentials of ...
5
votes
1answer
257 views

Why do Calabi-Yau manifolds crop up in string theory, and what their most useful and suggestive form? [duplicate]

Why do Calabi-Yau manifolds crop up in String Theory? From reading "The Shape of Inner Space", I gather one reason is of course that Calabi-Yaus are vacuum solutions of the GR equations. But are there ...
3
votes
1answer
310 views

Why is Compactification restricted to Toroids, Calabi-Yau et al?

I think I've missed this point somehow. I've just started with Compactification and so far, I don't really see why it is restricted to the above mentioned types of manifolds? I have to admit, when ...
6
votes
3answers
434 views

Why (in relatively non-technical terms) are Calabi-Yau manifolds favored for compactified dimensions in string theory?

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 ...
9
votes
1answer
307 views

Measurement of kaluza-klein radion field gradient?

I've been very impressed to learn about kaluza-klein theory and compactification strategies. I would like to read more about this but in the meantime i'm curious about 2 different points. I have the ...