# Questions tagged [kaluza-klein]

Kaluza-Klein theory is a classical theory that unifies gravity and electromagnetism by showing that general relativity in 5-dimensions reduces to the equations of 4-dimensional general relativity and the Maxwell equations in 4 dimensions.

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### If mass density curves space-time, then why isn't density (at each $x$, $y$, $z$) considered a dimension in space-time? [closed]

From http://science.howstuffworks.com "Theodor Kaluza theorized that a fourth spatial dimension might link general relativity and electromagnetic theory. But where would it go? Theoretical ...
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### Kaluza-Klein in superstring theory

In superstring theory, it says that they wrap 16 dimensions on a torus given by $\mathbb{R}^{16}$ divided by a SO(32) or $E_8 \times E_8$ lattice and this gives a gauge group of the same name. But in ...
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### Generalising a finding in Kaluza-Klein theory to extra spatial dimensions in super string theory a correct method?

As a disclaimer I am an A-level student. I have been doing a research project in which I am looking at manipulating space-time through the ideas provided by superstring theories. I stumbled upon the ...
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### A question about Kaluza-Klein mechanism

We know that there is a kind of compactification mechanism named Kaluza-Klein theory which states that the extra dimensions can be compacted dimensions such as $T^n$ or $S^n$ and so on. To make the ...
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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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### 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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### 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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### Dimensional Reduction for scalar fields

The main motivation for this question is the paper "Supersymmetric Yang-Mills Theories" by Brink, Schwarz and Scherk where they use dimensional reduction to go from Yang-Mills in $D=4$ to $D=2$. But ...
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### 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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### Doesn't modelling using Lie Groups assume spacetime is continuous?

Lie groups are used to some behaviors of quantum mechanics, as well as forming a basis for Kaluza-Klein, Yang-Mills, and String theory. But Lie groups are defined as involving a differentiable ...
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### Kaluza Klein Equations of Motion

I have found a derivation of the Kaluza-Klein equations of motion on this webpage: http://www.konfluence.org/Williams_31Mar2012.pdf As I understand it, he starts with the 5d geodesic equation of ...
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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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### Momentum and Kaluza-Klein charge

In normal Kaluza Klein reduction over a $S^1$, the momentum round the circle contributes to the electric charge in the lower dimensional theory. I am curious as to whether, under certain ...
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### Kaluza Klein charge

If I take a $(d+1)$ dimensional Einstein Hilbert Lagrangian $L_{d+1}=\sqrt{-\hat{g}} \hat{R}$ and perform a standard Kaluza Klein dimensional reduction by periodically identifying one direction, let's ...
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### $n=0$ 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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### What does Kaluza-Klein theory say about the attraction/repulsion of opposite/same charges?

Since Kaluza-Klein theory is made out of general relativity - a gravitational theory in 4 dimensions which is only attractive, then how does it takes into account the attraction/repulsion of opposite/...
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### Regge trajectory and Kaluza Klein tower

The mass of hadrons in the Regge trajectory scales as $m=\sqrt{\frac{J}{\alpha}-\alpha_0}=\sqrt{\frac{n}{\alpha}-\alpha_0}\propto \sqrt{n}$, where $J=n$ is the spin of the particle (in natural units,...
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### Lagrangian for $\mathcal{N}=4$ SQED in 3D

What is the Lagrangian for $3D$ $\mathcal{N}=4$ supersymmetric QED, with $N_f$ hypermultiplets? In particular, which is the form of the Fayet-Iliopulos terms, and the real mass terms?
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### 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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### Is there some no-go theorem for $D=9$ Kaluza Klein QCD+EM?

While QCD is a typical product of AdS/CFT and some other research trends in extra dimensions, I have never found in the literature an example producing the non-chiral part of the standard model, ...
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### Are all elementary interactions arising from a gauge theory?

The standard model of particle physics is based on the gauge group $U(1) \times SU(2) \times SU(3)$ and describes all well-known physical interactions but with exception that gravity isn't involved. ...
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### Can anyone explain to a novice physicist whether there is a gravitational-electromagnetic symmetry?

I am trying to understand how the four fundamental forces relate to one another and to a theory of everything. As I understand it the unified force that is thought to exist at very high energies gets ...
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### How to imagine higher dimensions?

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{...
### Basic question about curved and flat indices, and the Dirac matrices on $S^5$
In discussing the Kaluza-Klein formalism for Type IIB Supergravity on $S^5$, or the AdS5xS5 compactification, one requires Killing spinors on $S^5$. I read that the Dirac matrices on $S^5$ satisfy ...