# Tagged Questions

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4answers
10k 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 ...
4answers
2k views

### Shape of the universe?

What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand ...
8answers
5k views

### Why are extra dimensions necessary?

Some theories have more than 4 dimensions of spacetime. But we only observe 4 spacetime dimensions in the real world, cf. e.g. this Phys.SE post. Why are the theories (e.g. string theory) that ...
1answer
351 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 ...
0answers
235 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 ...
1answer
2k 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 ...
2answers
389 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 ...
1answer
342 views

### Measurement of kaluza-klein radion field gradient?

I've been very impressed to learn about kaluza-klein theory and compactification strategies. I would like to read more about this but in the meantime i'm curious about 2 different points. I have the ...
1answer
78 views

1answer
154 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 ...
0answers
51 views

### What is the importance of studying degeneration on $M_g$

Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$. It seems to be important in physics to study ...
2answers
2k views

### How can one imagine curled up dimensions?

Actually I'm learning String Theory, and one of its proposals is that there are actually 25+1 dimensions of which only 3+1 are visible to us-- and the remaining are curled up. However, superstring ...
1answer
433 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 ...
1answer
538 views

### CY moduli fields

When one does string compactification on a Calabi-Yau 3-fold. The parameters in KÃ¤hler moduli and complex moduli gives the scalar fields in 4-dimensions. It is claimed that the KÃ¤hler potentials of ...
1answer
454 views

### Why do Calabi-Yau manifolds crop up in string theory, and what their most useful and suggestive form? [duplicate]

Why do Calabi-Yau manifolds crop up in String Theory? From reading "The Shape of Inner Space", I gather one reason is of course that Calabi-Yaus are vacuum solutions of the GR equations. But are there ...
3answers
136 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{...
1answer
635 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 ...
1answer
151 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 ...
3answers
385 views

### What does string theory say about the metric expansion?

Specifically, what happens to those small intertwined hidden dimensions? Do those expand too?
0answers
115 views

### Calabi Yau compactification based on U(1) charges

In Green-Schwarz-Witten Volume 2, chapter 15, it is argued (roughly) that we need 6-dimensional manifolds of $SU(3)$ holonomy in order to receive 1 covariantly constant spinor field. And it turns out ...
2answers
409 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 ...
2answers
144 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 ...
1answer
307 views

### Could the 6 extra dimensions in superstring theory be a product of two manifolds?

Could the 6 extra dimensions in superstring theory be a product of two manifolds?
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 ...
2answers
178 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?
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 ...
1answer
78 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 Model,...
1answer
98 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 ...
2answers
133 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 ...
2answers
191 views

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 $\varphi(x) \... 1answer 86 views ### IIA and IIB Compact on 8D How can compactifying IIA (non-Chiral) and IIB (Chiral) Superstring on$T^2$(2-torus) gives rise to ($2$dual descriptions of) the same$\mathcal N = 2$supergravity in$8$dimensions? I don't see it.... 1answer 375 views ### Why is Compactification restricted to Toroids, Calabi-Yau et al? I think I've missed this point somehow. I've just started with Compactification and so far, I don't really see why it is restricted to the above mentioned types of manifolds? I have to admit, when ... 2answers 56 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 ... 1answer 271 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 functions(... 0answers 83 views ### Clarification on the 11 dimension in the M-theory [closed] In the book the Grand Design by Stephen Hawking, he wrote about the M-theory, and how in that theory it has 11 dimensions. I do not quite get that, so can someone explain it to me a little bit. I ... 0answers 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 ... 0answers 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 ...