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Articles discussing examples of Kaluza-Klein Reduction

The notes for my class on Kaluza-Klein reduction are a bit all over the place and at times it's difficult to follow what's going on. (I plan on asking a specific question about an example later). For ...
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1answer
43 views

$n=0$ mode Fourier expansion on string theory

I am quite baffled at what the $n=0$ mean in compactification, why is this mode important? I mean if $n=0$ was applied here we'd just be left with I know that (39) holds from (37), but I can't ...
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0answers
40 views

What are the definitions and the differences between string “background” and string “vacuum”?

In cosmology one studies perturbations around FRW metric classically (pure GR, we say that we perturbe the FWR "background"). In QFT we have perturbation theory quantistically (we expand around a ...
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3answers
347 views

The size of extra dimensions

Supposing we have a model, like the String one, which predicts (or requires) $N$ spacetimes dimensions, for the precision let's talk only about space dimensions. What is the process, the rule or the ...
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2answers
94 views

Is it possible to calculate the shape of extra dimensions?

According to Brian Greene it is possible to calculate the physical constants from the shape of the extra dimensions. Is it possible to do the inverse, so predict the shape of these dimensions from the ...
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37 views

M-theory compactified on $S^4$

I am trying to understand what happens to the 32 supersymmetries of M-theory when it is compactified on $S^4$, with the other seven dimensions being flat, e.g., $\mathbb{R^7}$, $\mathbb{R^6} \times ...
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1answer
57 views

In M-theory, are strings created by membranes?

In M-theory there are 2- and 5-branes, but where are the one-dimensional strings which are responsible for all the particles? Can 5-branes turn into 1-dimensional strings due to compactification?
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17 views

Toroidal compactification and number of susy

In case of Tordial compactification, reference states page 13, A.Font et al, Introduction to string compactification, it does not reduce the number of real supercharges. I wonder why this happens. ...
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1answer
82 views

Calabi Yau Motivation

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 ...
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1answer
46 views

Can you compare curvatures in space, spacetime and hidden space?

Spacetime curvature is given by the cosmological constant, that produces a De-Sitter spacetime. It is non-zero. But space curvature is nearly zero (how close to zero, compared to the cosmological ...
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0answers
40 views

Type I string theory on $K3 \times \mathbb T^2/\mathbb Z_2$ and the K3 orbifold limit

Consider Type IIB string theory with 4 O7-planes and 32 D7-branes on $K3 \times \mathbb T^2/\mathbb Z_2$. The K3 induces D3-charge on their world-volumes which can be cancelled by the introduction of ...
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74 views

Projector and delta function on a cycle $\Sigma$ of a manifold $\mathcal{M}_6$

In the paper ``Hierarchies from Fluxes in String Compactifications'' by Giddings, Kachru and Polchinski, the following example is considered for a localized source that may have negative tension (my ...
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1answer
77 views

Question regarding moduli space of a Calabi-Yau manifold

On page 132 of "Introduction to Supergravity" by Horiatiu Nastase, the author says: On $M = CY_3$ (Calabi-Yau space) there are $b_3$ topologically nontrivial 3-surfaces, for which we can define a ...
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0answers
40 views

Need explanation for $CY_3$ folds comes first rather than algebraic curves comes first [duplicate]

The example I am aware of so far is quintic 3-fold equipped with $SU(3)$ holonomy. Why it is more natural to talk about $CY_3$ folds or Calibi-Yau 3 folds without talking about algebraic curves in ...
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3answers
883 views

How to imagine higher dimensions?

In the link below Carl Sagan described about higher dimension: http://www.youtube.com/watch?v=UnURElCzGc0 and here's a description of Brian Greene: http://www.youtube.com/watch?v=v95WjxpMIQg Carl ...
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1answer
128 views

Ernst potential from Kaluza-Klein reduction of axisymmetric space-time

Following appendix A of "Ergoregions in Magnetised Black Hole Spacetimes" by G. W. Gibbons, A. H. Mujtaba and C. N. Pope, starting from the Lagrangian $$\mathcal{L} = \hat{R} - ...
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1answer
127 views

Why is the torus important for compactification in string theory? (aka much ado about the torus)

Why is the torus important in string theory and supergravity? To be specific, why does one care about something like compactification of Type IIB or IIA supergravity on a torus $T^5$, as opposed to ...
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2answers
144 views

Idea behind Compactified Boson

On p. 167 of his Conformal Field Theory, Di Francesco introduces "Compactified Boson". He says: The invariance of the free-boson Lagrangian [...] with respect to translations $\varphi(x) ...
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1answer
148 views

How can extra (non-curled up) dimensions be hidden from us?

Wikipedia says: If extra dimensions exist, they must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny ...
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1answer
143 views

Compactified extra dimensions and symmetry

It's my understanding that M-Theory necessitates 11 space-time dimensions (10 spatial dimensions plus 1 time dimension) in order work mathematically. This appears to jar with reality, which only ...
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1answer
225 views

$U(1)$ 5-dimensional Kaluza-Klein topological defects

Five-dimensional Kaluza-Klein theory is well-known to predict that the electromagnetic field can be described as a curled additional dimension over four-dimensional spacetime. That is, you only need ...
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1answer
357 views

What is dimension and how many types of dimensions are there in the universe?

What is dimension and how many types of dimensions are there in the universe? I mean how many total dimensions are there? I have only heard about 2d and 3d. Other than these two, are there any other ...
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0answers
87 views

Can spin angular momentum be understood as orbital angular momentum in extra dimensions?

It is to my understanding that in Kaluza-Klein theories the mass of particles can be understood as linear momentum in the extra dimensions. Let's consider in $\mathbb{R}^{1,3}\times{}B$ space-time a ...
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3answers
124 views

Justification of not quantizing small extra dimensions

When dealing with extra dimensions ($ x ^\mu $ represents $ 4D $ spacetime and $ y $ the extra dimension) we use what's known as Kaluza-Klein decomposition (basically a Fourier transform), ...
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1answer
372 views

Do we exist in multiple dimensions?

I have heard that there are 12 spatial dimensions. Does this mean that this many are possible, or that 12 dimensions actually exist? If the latter, then do the same things that exist in 3 dimensions ...
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1answer
164 views

Calabi-Yau condition, moduli and Lichnerowicz equation

I have a conceptual confusion about the metric moduli of Calabi-Yau manifolds, when I was reading Calabi-Yau compactification. As I understand, the metric moduli is parametrized by infinitesimal ...
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1answer
55 views

Coordinates of the extra dimensions

If we live in more than three spatial dimensions, is it not right to conclude that all matter observable to us shares almost the same coordinates of extra dimensions. Or is it just that ordinary ...
2
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1answer
79 views

The equivalence of two worlds related by T-duality

T-duality in string theory relates a world containing open and closed strings with a D$p$-brane with a compact dimension with radius $R$ with a dual world with a D$(p-1)$-brane with a radius ...
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0answers
67 views

In KK theory, is proper time defined using the 5 dimensional or the 4 dimensional line element?

Let's consider five dimensional KK theory. This is Klein's metric $\hat{g}_{AB}= \begin{pmatrix} g_{00}+A_{0}A_{0}&g_{01}+A_{0}A_{1}&g_{02}+A_{0}A_{2}&g_{03}+A_{0}A_{3}&A_ 0\\ ...
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1answer
290 views

Can the compactified dimensions of M-Theory/String Theory become uncurled?

Is it possible for the curled dimensions described in superstring theories to become uncurled and open up. I have read that the big bang could have been the uncurling over 3 dimensions through ...
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0answers
70 views

Compactification and off-diagonal terms of the metric tensor

In standard 3+1 dimensional spacetime, the metric tensor is of order 4 and had ten independent coefficients, hence there are 6 terms off the diagonal in the corresponding $4\times 4$ real symmetric ...
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2answers
169 views

Ricci flat compact manifold with $U(1)\times{}SU(2)\times{}SU(3)$ isometry group?

As the title says, is it possible to have a Riemannian Ricci flat compact manifold with $U(1)\times{}SU(2)\times{}SU(3) $ isometry group?
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66 views

A question on the Bousso-Polchinski paper

In this famous paper by Bousso and Polchinski, Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant an example in M-theory compactification is given in section ...
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2answers
105 views

Is any one compact dimension for one particle the same as for another particle?

In the 3+1 dimensions of everyday life and GR particles can share the same extended dimensions. Probably all particles share the same 3+1 dimensions. In string theory compact dimensions seem to be ...
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3answers
452 views

Is there any intuitive interpretation of compactification?

Obviously the question's title has an unspecified subtext: intuitive to me. Some background to pitch the discussion appropriately: I have a broad understanding, more qualitative than quantitative, of ...
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0answers
44 views

What is 'heterotic string compactification'?

I've read that some exceptional groups arises in the context of 'heterotic string compactification'. Could someone explain (to a person studying physics but who doesn't know string theory) what ...
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0answers
73 views

Laplacian in 4 spatial dimensions; 4th dimension warped

How can I prove the form of the Laplacian in four spatial dimensions, using the identification $y = y + 2\pi R$ for the fourth dimension and assuming the others as the usual Cartesian ones? I want to ...
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2answers
138 views

$D$-brane and 5th dimensions

While I was looking up the 5th dimension of the Randall-Sandram model, I have wondered whether Kaluza Klein theory can be applied to the $D$-brane or $p$-brane. Can the $D$-brane and $p$-brane ...
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0answers
38 views

Compact manifold taken as an Einstein Manifold

In Kaluza-Klein theories I often see that the compact space is assumed to be an Einstein manifold, that is, its Ricci tensor is proportional to its metric. So, why is this done?
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1answer
281 views

Spin connection in higher dimension

I have a problem regarding computation of spin connection in the case where One or more dimension is compactified. For example if we take a $D+1$ dimensional bosonic string action and write the $D+1$ ...
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1answer
130 views

Where do our 4 macroscopic spacetime dimensions reside in multidimensional models of the universe?

In models such as M-theory with 7 'higher dimensions' plus the 4 macroscopic spacetime dimensions, where do our 4 macroscopic spacetime dimensions reside ordinally? My reason for asking is TV shows ...
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1answer
532 views

Kaluza Klein theories, dilation field, and dimensional reduction

I am reading something about Kaluza Klein theories and compactification. I have some conceptual question: (1) Why do we call the fifth scalar field $\Phi$ the dilation field? Is there any scaling ...
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2answers
395 views

What Does it Mean for an Extra Dimension to Have Size?

Recently I watched this presentation by Brian Greene on string theory. In it he describes how the reason we don't observe the extra dimensions required by string theory could be because they are very ...
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1answer
77 views

What is the need to consider a singular spacetime?

To have a consistent superstring theory (which is to avoid the conformal anomaly on the worldsheet CFT) we are forced to build our theory on the critical dimension $n=10$. However, the Standard ...
5
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1answer
139 views

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 ...
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2answers
231 views

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 ...
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1answer
260 views

Effective action for bosonic string theory with enhanced symmetry

See these lecture http://members.ift.uam-csic.es/auranga/lect7.pdf page 17. Usually one derives the effective action from the massless states calculating amplitudes, otherwise through beta ...
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1answer
157 views

Betti multiplets in Kaluza Klein compactifications

It is well known that if the compactification manifold of a supergravity theory has non-zero Betti numbers, this may lead to the so called Betti multiplets in the spectrum of the low dimensional ...
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1answer
1k views

Gravitational constant in higher dimensions?

From Newton's law of gravitation we know that $$F=G\frac{m_1m_2}{r^2}$$ where $G$ is gravitational constant. We can also see that it has dimensions $$[G]=\frac{[L]^3}{[M][T]^2}$$ and we have a ...
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2answers
602 views

Is there an intuitive way of thinking about the extra dimensions in M-Theory?

Why are 11 dimensions needed in M-Theory? The four I know (three spatial ones plus time) have an intuitive meaning in everyday life. How can I think of the other seven? What is their nature (spatial, ...