# Questions tagged [compactification]

Compactification entails changing a theory with respect to one of its space-time dimensions. Instead of this dimension ranging to infinity, the theory is changed so that this dimension has a finite range, and may be periodic. In the limit where the size of the compact dimension goes to zero, no fields depend on this extra dimension, and the theory is *dimensionally reduced*. Further use for dimensional reduction.

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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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### Why is (1,1) worldsheet SUSY enhanced to (2,2) SUSY after compactification of type II string theory on a CY threefold?

I have a quick question. In case of compactification on an Calabi Yau cutting off 3/4th SUSY from the type-II string in 10D leads to an enhancement of worldsheet SUSY. It has been claimed since time ...
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### String Compactification on a Circle Results in a Moduli Space?

I have been reviewing some string theory for a project I'm working on and I have some questions regarding string compactifications on a circle and the precise definition/origin of the moduli space ...
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### The M2 brane of M theory creates the Type IIA string and D2; the M5 brane creates the D4 and NS5. What are the other objects grouped with the D0?

Type IIA string theory is related to M theory with the 10th spatial dimension compactified on a circle.  The origin of the F1 string, D2 brane, D4 brane and NS5 branes is simple: they come from the M2 ...
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### Are "Selective Extra Dimensions" possible?

The large extra dimensions model also known as the ADD model proposes that the six hidden dimensions implied by string theory are not rolled up to the Planck length and some (or all) of them are ...
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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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### Motivation of Keeping Supersymmetry in String Compactification

In Candelas, Horowitz, Strominger, and Witten's famous paper  about string compactification, they ask that supersymmetry should not be broken in the resulting 4d theory. Then combined with other ...
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### Is classical Kaluza Klein theory stable or not?

Set Up In the original classical Kaluza Klein theory, you have a $d+1$ dimensional manifold where one space dimension is a circle $S^1$. In the "low energy limit," none of the metric ...
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### Twistor and Calabi-Yau spaces

The twistor space of Penrose's twistor theory is a projective space of three complex dimensions. This can be understood as six orthogonal dimensions, three with real metric and three with imaginary ...
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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 ...
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### $T$-duality in effective gauge theories of a $D(p+1)$-brane

I am considering a $D(p+1)$-brane in a space $\mathbb R^{1,p}\times S_R^1$ where $S_R^1$ is the circle of radius $R$. I am assuming low energies $ER\ll1$, so that only the massless spectrum of the ...
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### Rolled-up dimensions vs surfaces in a higher dimensional space

All the accounts of dimensions higher than 4 seem to talk about them being 'rolled up'. Is this different to being confined to a 4D surface that exists in a higher dimensional space?
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### How and why does toroidal compactification fail to capture observed physics?

My question is motivated by a statement in this chapter (emphasis added, off-topic statements about supersymmetry elided): Compactifying on tori ... is very interesting for its simplicity ... but not ...
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### How many fields are there in most flux compactifications?

Quoting from this paper: At first sight, the most striking thing about these compactifications is how many fields they have compared to the Standard Model. While the particle physicists of the 1930s ...
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### What are compact dimensions in string theory?

It is often said that string theory describes the world at the most fundamental level and is independent of the background, that is, not the strings are in space-time, but the space-time itself is ...
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### Compactification of additional dimensions [duplicate]

The extra dimensions in string theory are supposed to close in on themselves to form circles. Are there other possibilities for compactification? For example a compactification in segment.
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### Can string theory be background independent?

Are there any models in string theory which are background independent? If there are, would this mean that these models could be built in any number of dimensions? (Instead of assuming a fixed number ...
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### Different symmetries or no symmetries in string theory?

I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention: At page 195 the authors say that universes with different symmetries could ...
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### Might the Kaluza-Klein scalar provide a solution to the dark puzzles?

Kaluza-Klein theories of a five-dimensional spacetime yield not only the equations of general relativity and electromagnetism, but also a scalar field. This scalar field, sometimes quantised as the ...
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### String Theory for beginners: what is a scale?

I'm reading this introduction to string theory by Mariana Grana and Hagen Triendl and I have understanding problems around the method of compactification in string theoretical sense. The ...
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### Polchinski String Theory (8.4.38) T-duality of two compactified dimensions

I am confused about a sentence in Polchinski's String theory chapter 8 p 255 when he works out the example of the full $T$-duality with two compact dimensions. He writes "A simultaneous $T$-...
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### How to test extra dimensions?

It is predicted in string theory that our world has some extra dimensions. I'm wondering if we want to prove this experimentally, what should we do
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### How to compute Physical Constants from given Calabi-Yau Compactification of Effective Field Theory of corresponding String Theory?

I got some interest in String Theory when I was listening to lectures of David Tong and Brian Greene. I remember them stating that the spacetime manifold is compactified to resemble our usual 3+1 ...
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### Alternatives to Calabi-Yau spaces? [duplicate]

Are there alternatives to Calabi-Yau spaces describing dimensions in superstring theory? If yes, what are they? If no, why?
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### Dimensional regularization and (dimension) compactification [closed]

I believe I read that "additional dimension" in dimensional regularization can be understood as spatial dimensions compactified, but I could not find resources related to this. Is this view correct? ...