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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.

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.

Compactification plays an important part in thermal field theory, where time is compactified; in string theory, where one compactifies the numerous extra dimensions of the theory; and in two- or one-dimensional solid state physics, where one considers a system limited to one of the three standard spatial dimensions.

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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 require more dimensions taken seriously by scientists?…
Fakrudeen
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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 equally everywhere in all directions. But they also…
TROLLHUNTER
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Why does string theory require 9 dimensions of space and one dimension of time?

String theorists say that there are many more dimensions out there, but they are too small to be detected. However, I do not understand why there are ten dimensions and not just any other number? Also, if all the other dimensions are so coiled up…
James Kujareevanich
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Why is full M-theory needed for compactification on singular 7-folds and what does that even mean?

In "M-theory on manifolds of $G_2$ holonomy: the first twenty years" by Duff, it is claimed (e.g. in section 8) that for compactification on singular 7-folds to be possible, we need to consider not the 11D supergravity (SUGRA) approximation to…
ACuriousMind
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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 good numerical estimate of its value ($G\simeq…
dingo_d
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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 will of course remain in the NS sector. I am…
Ryan Thorngren
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Could mass just be light moving in another dimension?

Could mass just be perceived as light moving along a geodesic through an additional spatial dimension (either invisible or somehow curled up into itself)? Since the light would be moving in another dimension, to us its velocity will be less than the…
Tachyon
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What is the stringy interpretation of the cohomology classes arising from the Kähler class?

In superstring theory, one usually considers compactifications on Calabi-Yau 3-manifolds. These manifolds are in particular compact Kähler, hence possess a Kähler class which gives rise to nontrivial cohomology classes in every even degree. To see…
Danu
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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 on its implied interaction with normal 3+1…
Argus
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How does one actually apply the M-theory/heterotic duality "fiberwise"?

It seems to be generally accepted ([1], [2]) that one can apply the duality between a $T^3$ compactification of heterotic string theory and a $\mathrm{K3}$ compactification of M-theory "fiberwise" to dualize a heterotic compactification on a…
ACuriousMind
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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 dimensions out there (often talked about in…
ZECTBynmo
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Why (in relatively non-technical terms) are Calabi-Yau manifolds favored for compactified dimensions in string theory?

I was hoping for an answer in general terms avoiding things like holonomy, Chern classes, Kahler manifolds, fibre bundles and terms of similar ilk. Simply, what are the compelling reasons for restricting the landscape to admittedly bizarre…
Gordon
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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 understand what is really M-theory and why is…
Martin Hurtado
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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 feeling that there are no precise answers to these…
lurscher
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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 talking about detecting particles in extra…
ODP
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