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How To Arrive At Ground State Metric of Kaluza-Klein Theory

The ground state metric, after an extra dimension of space is compactified (to a circle) in Einsteinian gravity, is the metric which corresponds to the R_4 × S_1 geometry of the separated dimensions. ...
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1answer
49 views

The form of the metric after a dimension is compactified

Upon the compactifiation of one spatial dimension, it is said (as though an axiom) that the 5 dimensional spacetime metric separates into a 4 dimensional metric, a vector, and a scalar, (4D gravity, ...
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52 views

What does the geometry of a compactified dimension impact?

In Kaluza's original work, he didn't compactify the fifth dimension, rather imposed the "cylindrical condition" where none of the components in the 4D metric depended on the 5th dimension. It wasn't ...
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1answer
42 views

Do Calabi -Yau shapes also influence a strings particle identity?

Since strings reside on the surface of a d-brane, and it' a three dimensional hyperspace, are their manifestations as certain particles also influenced by Calabi Yau Spaces? Could the way strings ...
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1answer
29 views

Ground state metric?

In kaluza-klein theory, there's a notion of a "ground state metric" after compactification. What is the meaning of the term "ground state metric"?
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1answer
44 views

What relative effects be for object with near light speed velocity in compactified dimensions?

What relative effects be for an object with near light speed velocity in compactified dimensions? Does gravity increase the same as for an object with near light speed velocity in usual spacial ...
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1answer
74 views

Is most of what everything is made from in another dimension?

If there are eleven dimensions as M-Theory asserts would that mean that the majority of what we are made from exists in the seven other dimensions?
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2answers
22 views

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
51 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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44 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
377 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
134 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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0answers
41 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 S^...
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1answer
62 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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18 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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2answers
125 views

What is the motivation for using Calabi-Yau manifolds in string theory?

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
53 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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47 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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84 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
81 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
41 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
1k 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
165 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} - \hat{F}_{\mu\nu}\hat{...
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1answer
174 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
185 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
156 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
159 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
269 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
417 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
91 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
133 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), \begin{...
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1answer
407 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
177 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
57 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 ...
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1answer
82 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 $R'=\...
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0answers
70 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\\ g_{10}+...
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1answer
307 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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74 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
176 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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0answers
70 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
113 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
545 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
45 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 ...
2
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0answers
81 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
143 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
306 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 $D+1$ ...
2
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1answer
141 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
619 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
405 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 ...