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40 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 ...
5
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3answers
104 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
120 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 ...
2
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1answer
101 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
41 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
66 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 ...
2
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0answers
46 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\\ ...
2
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1answer
216 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
42 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 ...
3
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1answer
113 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?
3
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0answers
39 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
67 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
152 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 ...
2
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0answers
35 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
53 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 ...
3
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2answers
89 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 ...
1
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0answers
26 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?
2
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1answer
174 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
101 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 ...
5
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1answer
230 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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3answers
252 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 ...
3
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1answer
67 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
100 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
193 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 ...
3
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1answer
232 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 ...
7
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1answer
134 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 ...
8
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1answer
648 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 ...
7
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2answers
515 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, ...
0
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0answers
53 views

Extra dimensions and the big bang [duplicate]

If there were extra compact dimensions,and at the big bang all dimensions were compact,my question is why the big bang failed to expand those presumed extra dimensions like it did with the 3 spatial ...
1
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1answer
155 views

Dimension & non - locality problem in string theory

I have some questions with string theory: Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR?
5
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3answers
319 views

What does string theory say about the metric expansion?

Specifically, what happens to those small intertwined hidden dimensions? Do those expand too?
5
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1answer
289 views

${f=ma}$: a duality between F-theory and M-theory?

$$F = M \Big|_{A(T^2) \to 0}$$ The above equation is the duality equation between F-theory and M-Theory on a vanishing 2-torus. What's the explanation for this equation? Is there anything similar ...
1
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1answer
119 views

Relationship between lightlike and spatial compactification

The compactification of a spatial dimension, say $x^1$ given by the identification $x \sim x^1 + 2\pi R$ is said to be related to the lightlike compactification by a Lorentz boost : $$ \left( ...
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1answer
195 views

How exactly are Calabi-Yau compactifications done?

To compactify 2 open dimensions to a torus, the method of identification written down for this example as $$ (x,y) \sim (x+2\pi R,y) $$ $$ (x,y) \sim (x, y+2\pi R) $$ can be applied. What are the ...
3
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1answer
78 views

IIA and IIB Compact on 8D

How can compactifying IIA (non-Chiral) and IIB (Chiral) Superstring on $T^2$ (2-torus) gives rise to ($2$ dual descriptions of) the same $\mathcal N = 2$ supergravity in $8$ dimensions? I don't see ...
0
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0answers
56 views

What is the effect of the compact extra dimensions of the heterotic theories?

The five super-string theories are generally said to be 10-dimensional. However the Heterotic theories combine a bosonic left mover (which lives in 26 dimensions) with a super right mover (which lives ...
3
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1answer
83 views

Must string models that describe 4d effective field theories always have D-branes that extend in the 4 non-compact spacetime dimensions?

In string theory the D-branes give those directions that the strings are allowed to move along. The string excitations give the fields that we detect. Is it correct to think of a particle propagating ...
2
votes
1answer
189 views

Why do the mismatched 16 dimensions have to be compactified on an even lattice?

The mismatched 16 dimensions between the left- (26 dimensional) and right- (10 dimensional) are compactified on even, unimodular lattices. I think I get the unimoduar part, at least intuitively, ...
0
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1answer
154 views

How many dimensions are there in total? [duplicate]

I happened to get my hands on a string theory book where its been said that the universe's fundamental particle i.e. the string, takes about ten dimensions for specifying itself under symmetry. What ...
1
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1answer
223 views

Calabi-Yau manifolds and compactification of extra dimensions in M-theory

I just finished learning M(atrix) theory and the basics of the compactification of extra dimensions. The extra 6 dimensions of superstring theory can be compactified on 3 Calabi-Yau manifolds ...
1
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1answer
160 views

Type I' String theory as M-theory compactified on a line segment?

I was considering the S-dual of the Type I' String theory (the solitonic Type I string theory). That is the same as the S-dual of the T-Dual of Type I String theory. Then, that means both length ...
2
votes
1answer
135 views

Current operators for compactified CFTs

Intuitively I feel that if you compactified open bosonic strings on a product of $n$ circles such that each radius is fine-tuned to the self-dual point then the CFT of these $n$ world-sheet fields ...
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0answers
197 views

Compactifying on a circle and the exchange of R and NS sectors

I've noticed a general phenomenon in compactifying on a circle where if you start with, say, an NS field, then the KK fields with an index along the circle will be in the R sector, and those without ...
12
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1answer
306 views

How can two time theories be compactified to 3+1 without any Kaluza-Klein remnants

I have recently been looking into the two-time theories and the implied concepts. For me this seems slightly hard to grasp. How can I see the basic concept in this theory in a fundamental way based ...
2
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0answers
117 views

Can decompactification explain the inflation of the early universe?

I've just reread chapter 11 of this book where it is explained among other things, that our four dimensional universe could be unstable concerning a decompactification transition, since potential ...
6
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1answer
132 views

Disappearance of moduli for condensate of open strings

Consider a Dp-brane. Compactify $d$ spatial dimensions over a torus $T^d$. Suppose $d\geqslant p$, and that the Dp-brane is completely wrapped around the compactified dimensions. Look at the open ...
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0answers
97 views

Examples of manifolds and fluxes coming from generalized complex geometry

The paramount object in generalized gomplex geometry is the Courant algebroid $TM\oplus T^\star M$, where the manifold $M$ is called background geometry I think (I am not sure). More generally this ...
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0answers
121 views

Folded and/or compacted dimensions in M-theory?

I've on many occasions that there are various numbers of 'extra' dimensions above the 4th. However, I've heard that they are 'compacted' or 'folded' tightly and unimaginably small. Now, as I ...
7
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2answers
245 views

Why would a particle in an extra dimension appear not as one particle, but a set of particles?

I was reading an article in this months issue of Physics World magazine on the three main theories of extra dimensions and stumbled across something I didn't quite understand when the author began ...
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4answers
5k views

Is spacetime discrete or continuous?

Is the spacetime continuous or discrete? Or better, is the 4-dimensional spacetime of general-relativity discrete or continuous? What if we consider additional dimensions like string theory ...