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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How can we know we have successfully formulated the M theory action?

There have been quite a few attempts at building the action for M theory, such as the various Matrix formulations, F theory and others. But what is a defining characteristic or mathematical test that ...
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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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Generating Fermions from Dimensional Compactification

The usual KK compactification generates additional scalar fields or gauge fields when off diagonal terms are considered in the metric. These fields have integer spin when quantized. Is it possible, ...
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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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71 views

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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475 views

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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65 views

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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115 views

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 ...
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138 views

Questions about the landscape in string theory

If I understand correctly, the string theory landscape is the totality of possible Calabi-Yau manifolds to make up the compact factor of space in string theory, in which there are of the order of $10^{...
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What is meant by this variant of the euclidean plane: $\mathbb{R}^2_{\hbar}$?

I am reading some papers in mathematical physics (https://arxiv.org/abs/1006.0977) and I came across the following symbol $\mathbb{R}^2_{\hbar}$ I don't recognize nor could I find any background ...
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Kaluza-Klein and Fourier expansion

In every book/reference on Kaluza-Klein (KK) dimensional reduction, one uses that fluctuations $\delta\Phi(x,y)$ can be expanded as follows $$\delta\Phi(x,y)= \sum_n\delta\Phi_n(x)\,h_n(y)$$ where $\{...
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What generates the curvature which is necessary for curling-up extra dimensions?

To say it right away, I am not an expert in string theory, but I know well General Relativity. So I wonder how the curling up of extra-dimensions which is assumed in many "Kaluza-Klein" like theories (...
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Understanding a joke in Zwiebach - “A first course in string theory” [closed]

So fairly early on Zwiebach discusses the quantum mechanics of a one-dimensional square well. He then goes on to add an extra dimension which is compact to demonstrate how one can understand ...
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How seriously should one take the energy eigenvalues of an electron's wavefunction in a compactified space?

In chapter 2 (section 2.10) of Zwiebach's string theory book, there is a neat derivation of the energy eigenvalues for the two dimensional square well in which one dimension is compactified to a ...
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Effective action of IIB Calabi-Yau compactification

I'm currently reading K. Becker, M. Becker and John. H. Schwartz book on string theory. I have a question about Calabi-Yau compactifications of IIB string theory. In chapter 9 page 403, Why do we don'...
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68 views

Compactification of Bosonic Closed Strings on $T^2$ and $T^3$

I am looking for a text to explain compactification of bosonic closed strings on $T^2$ and $T^3$ by focusing on its gauge groups enhancement. In fact, I want to know in each case ($T^2$ and $T^3$) how ...
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What is really M-theory? (non-pertubatively)

I don´t really understand what M-theory is supposed to be. Going beyond the dualities relating different string theories (for example the common $11-D$ limit of IIA and $E_{8}\times E_{8}$) I don't ...
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385 views

Algebraic geometry and topology for string theory [duplicate]

I am looking for a comprehensive book or notes in algebraic geometry and topology techniques used in string theory compactifications covering topics like orientifolds, orbiolds, Calabi Yau manifolds ...
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362 views

The role of the Hopf Fibration in Kaluza-Klein theory

I have been learning recently about the Hopf Fibration and its relation to physics. My professor has told me that it is one of the simplest methods of dimensional reduction in Kaluza-Klein theory. ...
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Can branes obstruct complex structure deformations in string theory?

In compactifications of string theory, to preserve supersymmetry often branes need to wrap subspaces that are specified by holomorphic equations in the compactification space $X$. Additionally there ...
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91 views

For making gravity supersymmetric is a modification of Einstein's vacuum field equations necessary ( apart from adding the R-S Lagrangian)?

Upon building up supersymmetric Supergravity in 4D, is it necessary to modify the Einstein's vacuum field equations (apart from adding the Rarita-Schwinger Lagrangian for the gravitino) in order to ...
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529 views

Where are the infinite-dimensional spaces of Quantum Mechanics?

There are two questions here: One of the confusing points about String Theory is the existence of extra dimensions. These are explained by saying that the these extra dimensions are compactified. ...