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.
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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 ...
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Do singular $G_2$-holonomy manifolds in M-theory have stable compactifications?
In this paper: Chiral Fermions from Manifolds of G2 Holonomy it is shown that compactifications of M-theory on a $7d$ $G_2$-holonomy manifold $X$, generate chiral fermions, if only $X$ is singular.
I ...
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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 ...
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The Z manifold and the corresponding Gepner and LG models
Let $\mathscr{T}$ be a product of three tori $\mathscr{T}_1 \times \mathscr{T}_2 \times \mathscr{T}_3$ with each torus formed by making the identifications $z_i \simeq z_i+1 \simeq z_i + \omega^{1/2}, ...
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The mirror of a rigid Calabi-Yau manifold
In various papers, I have seen descriptions that a rigid Calabi-Yau manifold has its mirror as a Landau-Ginzburg model.
Why do experts think this way?
Any comment welcome !
Thank you.
Edit: In ...
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Why the extra compact dimensions of superstring theory must form a Calabi-Yau manifold? [duplicate]
In superstring theory, extra dimensions are conjectured. Then, the obvious observation that, macroscopically, we observe only three spacelike dimensions and one timelike dimension, leads to the ...
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Calabi-Yau moduli space - Kahler metric deformations
On a Calabi-Yau manifold $(M,g)$, we have the requirement of Ricci-flatness of the metric $g$:
$$ R_{\mu \bar{\nu}}[g] = 0 $$
If we look at a deformation of the metric $ g + \delta g$ and impose the ...
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How can we prove this quintic is Calabi-Yau manifold?
Is there a simple proof that the following surface is Calabi-Yau? (i.e. it is Kahler and Ricci-flat?)
$$x^5+y^5+z^5+u^5+v^5=0$$
With $(x,y,z,u,v) \in \mathbb{CP}^4$.
Here are my conclusions and you ...
user84158
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Is it necessary that the compactified manifold in string theory must be complex?
I have learned that there are some restrictions imposed on the manifolds which are used to compactify the extra-dimensions of string theory. The most important being the "Ricci flatness" ...
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What is a specific example of a Calabi-Yau manifold? are there simple ones like a 6-torus, $T^6=(S^1)^6$ or $S^3\times T^3$
What is a specific example of a 6D Calabi-Yau manifold? are there simple ones like a 6-torus, $T^6=(S^1)^6$ , $S^3\times T^3$, or similar structures with products of Spheres and Torus?
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Can any other manifold be used for compactifying the 6 extra dimensions of string theory? [duplicate]
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 ...
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How many different vacua really are there in the string theory landscape?
How many different vacua are there in the string theory landscape? Different sources give different estimates: some sources talk about the number $10^{500}$, others $10^{272\ 000}$, still others say ...
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To what degree have Calabi-Yau manifolds been shown to be all linked by conifold transitions?
Originally, the number of Calabi-Yau manifolds (these are special vacuum solutions of Einsteins GR) was estimated by Yau to be a small finite number, later he revised it to be a large finite number - ...
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Structure of Planck volumes in String theory
This question (as the previous one) is mostly arose from such pictures:
As explained by Brian Greene, this is something what our Universe should look like at a Planck scales in superstring theories.
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How Strings move from 1 CY manifold to another?
M-theory says that there's a Calabi-Yau manifold, representing $n = 7$ extra spatial dimensions (here simplified to $n = 3$; check out animated video) curled up and compactified inside every 3D Planck ...
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