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Questions tagged [calabi-yau]

This tag should be used in the context of superstring theory or the geometrical shape. This tag should be used for Calibi-Yau manifolds and not other types of manifolds or Calibi-Yau algebra. Do not use this tag unless your question specifically asks about Calibi-Yau manifolds - this tag should not be added just because your question is about superstring theory.

Below is an example of a Calibi-Yau manifold.

Calibi-Yau manifold example

Calibi-Yau manifolds are a special type of manifold that can be described in certain branches of mathematics, such as algebraic geometry. The properties of Calibi-Yau manifolds lead to their application in theoretical physics, especially superstring theory. They are shapes that satisfy the requirement of compactification for the six "hidden" dimensions of superstring theory.

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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 restricting the landscape to admittedly bizarre…
Gordon
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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 feeling that there are no precise answers to these…
lurscher
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What is the motivation for using Calabi-Yau manifolds in string theory?

I have just begin to study Calabi-Yau compactification. Looking in many book I found that, if we start with a critical superstring theory in $D=10$, we are in search of a compact $D=6$ Calabi-Yau manifold, i.e. a manifold with a spinor that is…
MaPo
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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 definition of the concepts used is different than what…
Squark
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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 methods to compactify 6 open dimensions to a…
Dilaton
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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 knowledge in algebraic geometry and complex…
psm
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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 generalisations. From what I could surmise, its main…
Nihar Karve
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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 the CY moduli space gives the kinetic terms of the…
color
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Why do Calabi-Yau manifolds crop up in string theory, and what their most useful and suggestive form?

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 any other reasons? Also, given those reasons,…
John R Ramsden
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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 Euler number must be $\pm6$ so that it is…
Mathematician
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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 Kahler metric such that the holonomy group $G…
Mathematician
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How do compact dimensions determine the particle content of string theory?

In string theory, 10 spatial dimensions are required for mathematical consistency. One way to model our 3-dimensional universe is by compactifying the extra dimension on a Calabi-Yau manifold. They are 'flat enough' to be vacuum solutions to…
user34722
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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 that Calabi Yau manifolds satisfy this…
Frank Müpe
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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 studying T-Duality, I simply took Toroidal…
Michael
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Decomposition of vector bundle in $M$-theory

I was studying this paper where the authors construct some field theory solutions by wrapping M5-branes on holomorphic curves on Calabi-Yau. I have some questions about their construction. What they do is to consider the local geometry (2.1)…
Davide Morgante
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