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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Number of unbroken supersymmetries in compactifications

In type II compactifications, we take a 10/11-d spinor $\epsilon$ to decompose into internal $\eta$ and external $\zeta$ pieces, $$\epsilon^1=\zeta^1\otimes\eta^1\ \ (+c.c.)$$ $$\epsilon^2=\zeta^2\...
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Is it possible to have an unbroken SUSY and the superpartners are hiding because they travel sometimes to extra dimensions? [closed]

Is it possible to have an unbroken SUSY and the superpartners are hiding because they travel sometimes to extra dimensions? It is hard to lose SUSY so maybe SUSY Particles are just hiding in ...
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Do we have an upper bound to the size of the six hypothetical curled up dimensions in string theory?

String theory requires ten (or eleven for M-theory) extra dimensions. These dimensions are not observed at large scales and so it has been hypothesised that they are curled up and invisible at larger ...
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Basic confusion about interpretation of the 5th dimension in Kaluza-Klein theory

As has been mentioned in other posts, Kaluza originally didn't require the 5th dimension to be curled up/compactified. So how exactly would our 4D world emerge from a non-compactified 5D manifold? I ...
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Some questions about the compact boson in David Tong's notes on Gauge Theory

The notes can be found at http://www.damtp.cam.ac.uk/user/tong/gaugetheory.html. In Sec. 7.5.1, T-Duality, around Eq. 7.51, it says that the Bianchi identity $\partial_\mu(\epsilon^{\mu\nu}\partial_\...
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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 [1] 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? ...
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How to explain "compactification of a dimension"

The first paragraph of the wikipedia entry on "compactification (physics)" explains that it "means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with ...
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Is one dimension the same as one space-time?

In this Cern article, https://home.cern/science/physics/extra-dimensions-gravitons-and-tiny-black-holes, it states: "In our everyday lives, we experience three spatial dimensions, and a fourth ...
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Four dimensional massless spectra of type IIA/B compactified on $\mathcal{M}_{4} \times {\rm CY}_3$

I am following “String Theory and M-Theory” by Becker, Becker, and Schwarz and I am currently studying chapter 9. I have a question - or better yet a point of confusion - regarding the derivation of ...
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Holomorphic 3-form on Calabi-Yau compactifications

What is the natural scale of the holomorphic 3-form on a Calabi-Yau? $\Omega=\frac{1}{3!}\Omega_{abc} ~ dz^a\wedge dz^b \wedge dz^c$ $||\Omega||^2 = \frac{1}{3!}\Omega_{abc}\bar{\Omega}^{abc}$ ...
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Did Big-Bang dimensional-expansion initially occur stepwise, i.e 1 dimension at a time?

I’ve been investigating the topological Casimir effect from compactified dimensions as a mechanism to explain dark energy, and this raised a question I was hoping someone could shed some light on. I ...
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How can extra dimensions be small?

I have a super basic gap in my understanding of the theory of extra spacial dimensions - one piece of the explanation that never felt right. As I've heard it, it's theorized that there may be extra ...
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Orientability of compactified manifolds in string theory

Calabi-Yau manifolds in string theory are orientable (topologically you can make "handed" structures in them). Non-orientable manifolds are perfectly respectable (the projective plane is a basic ...
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Why doesn't string theory predict the existence of infinitely many elementary particles?

I'm a physicist, but my knowledge of string theory is extremely minimal. My naive conceptual understanding is that the vacuum is modeled as a certain topology (and geometry?) for the spacetime, and ...
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Does string theory really associate 6 dimensions to electromagnetism & the nuclear forces?

1) I understand string (superstring) theory often ends up with 10 dimensions, 9 space-like and 1 timelike. Typically I read that these are all associated to space-time. 2) So, I was interested when I ...
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How can we demand $N=2$ supersymmetry on the worldsheet?

I have been trying to understand why one should look into $c=9, N=2$ superconformal models like the Gepner models or the Kazama-suzuki models, and I am quite confused. This is what I understood from ...
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Why is the central charge $c=9$ supersymmetry in the internal manifold?

In [2] (abstract [here]) (https://inspirehep.net/record/245643?ln=en) they say that, when compactifying any superstring theory, the six dimensional internal manifold must have $N=2$ supersymmetry with ...
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Are extra dimensions timelike or spacelike?

In special relativity there is a clear difference between spatial and temporal dimensions of spacetime due to the Minkowski metric diag(-1,1,1,1). In higher dimensional theories (10- and 26-...
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Toroidal compactifications of type IIB string Theory and $SO(5,5)/(SO(5)\times SO(5))$ invariant 6D sugra action

It is usually stated that the compactification of (the bosonic part of the) type IIB ($D=10$, ${\cal N}=(2,0)$) supergravity on $\mathbb{T}^4$ gives a six-dimensional ${\cal N}=(4,4)$ supergravity ...
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What is dimension? What is the size of dimension?

Recently I heard a TED talk by Brian Greene where he was speaking about String Theory working on $(10+1)$ dimensions. Plus he said that we live in only in $(3 +1)$ dimensions. So where are others? ...
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Dimensional reduction of higher-dimensional Einstein-Hilbert action

I take a spacetime of the form $\mathcal{M}_{d+1}\times \mathbb{S}^n$, with $\mathcal{M}_{d+1}$ some generic non-compact $(d+1)$-dimensional spacetime and $\mathbb{S}^n$ an $n$-dimensional sphere, so ...
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Extra Dimensions (in String Theory) - What does it mean?

I have been reading a lot about string theory and the necessity of extra dimensions (particularly as visualized in Calabi-Yau spaces), as "curling-ups" in our apparently 3-dimensional (or 4-...
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Compactification of space in Hamiltonian formulation of Yang-Mills theory

I am reading David Tong's lecture notes on Gauge Theory where he talks about Hilbert space interpretation of Yang-Mills theories in Section 2.2 of Chapter 2. When discussing the gauge dependence of ...
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Relationship between compactification moduli and generations in standard model

The situation I am describing is a $10D$ heterotic string theory which is compactified on a Calabi-Yau to get a $N=1$, $4D$ effective theory. It is mentioned in Ashoke Sen's notes on string ...
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Are the "extra dimensions" in string theory universal?

Are the extra (compactified) dimensions from string theory universal, in that any particle/field with a sufficiently small enough wavelength will be able to propagate through them? The reason I want ...
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Root weights and states in orbifold compactifications

I have the following question regarding orbifold compactifications of the heterotic string: What is the relation between a certain representation and the weights of the root lattice? I mean: take ...
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Are particles of fields that arise from compactification and strings treated differently in string theory?

I am aware that particles in string theory are different vibrating modes of strings. I am also aware that compactification leads to emergent fields from the parts of the metric of the compactified ...
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How do we assign length to dimensions in string theory?

My current understanding of the variations of string theory includes the sentence "string theory needs (at least) 6 extra spatial dimensions to work, but because our observable universe consists ...