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.

29 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
16
votes
0answers
388 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 ...
8
votes
0answers
136 views

What is the difficulty in extending geometrodynamics to non-abelian fields?

In an attempt to widen my own horizons I've decided to educate myself in Wheeler's Geometrodynamics. In the so-called "already unified theory" one can essentially reproduce an electromagnetic field ...
4
votes
1answer
222 views

Dimensional reduction of higher-dimensional Einstein-Hilbert action

I take a spacetime of the form $\mathcal{M}_{d+1}\times \mathbb{S}^n$, with $\mathcal{M}_{d+1}$ some generic non-compact $(d+1)$-dimensional spacetime and $\mathbb{S}^n$ an $n$-dimensional sphere, so ...
3
votes
0answers
197 views

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 ...
2
votes
0answers
93 views

Kaluza-Klein and Fourier expansion

In every book/reference on Kaluza-Klein (KK) dimensional reduction, one uses that fluctuations $\delta\Phi(x,y)$ can be expanded as follows $$\delta\Phi(x,y)= \sum_n\delta\Phi_n(x)\,h_n(y)$$ where $\{...
2
votes
1answer
279 views

The role of the Hopf Fibration in Kaluza-Klein theory

I have been learning recently about the Hopf Fibration and its relation to physics. My professor has told me that it is one of the simplest methods of dimensional reduction in Kaluza-Klein theory. ...
2
votes
0answers
160 views

Dimensional reduction from even to odd dimensions and Chern-Simons terms

I'll be taking some Lagrangians from this paper to try and keep personal typos out of the discussion I have been looking at the dimensional reduction of Einstein-Maxwell-Dilaton theories and I am ...
2
votes
0answers
99 views

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 ...
2
votes
0answers
82 views

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?
2
votes
0answers
150 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 ...
2
votes
0answers
99 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}+...
2
votes
0answers
143 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 ...
2
votes
0answers
45 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
votes
0answers
267 views

Ricci scalar higher dimensions

I was wondering if there is a straightforward way to compute the Ricci curvature of a metric that has the form (à la Kaluza-Klein): $g_{MM}\equiv\begin{pmatrix}g_{\mu\nu}&g_{\mu i}\\g_{i\nu}&...
1
vote
0answers
31 views

How to derive the perturbativity condition of a simple Kaluza-Klein theory?

I thought that the simple $\lambda\phi^4$ theory in 4D is always perturbative if $\lambda<1$. Below equation 107.1, PDG review of extra dimensions says that the 5D Kaluza-Klein theory $$S_5=-\int ...
1
vote
0answers
56 views

Kaluza-Klein approach and Gauss-Cadazzi approach

Can you tell me the difference or physical application of Kaluza Klein approach and Gauss Codazzi approach? In Kaluza Klein theory, 5 dimensional theory can be dimensional reduced to 4 dimensional ...
1
vote
0answers
71 views

Lifting 3d Chern-Simons theory to 4d

For simplicity, let us only consider abelian Chern-Simons theory. The usual way of lifting 3d Chern-Simons theory to 4d is achieved through the Stokes' theorem. Say, if the original Chern-Simons ...
1
vote
0answers
91 views

Attempt to understand the Kaluza-Klein theory

I'm currently doing an internship on Kaluza-Klein theory. by reading some articles, I don't understand some things that seem easy to authors for example : In this article https://arxiv.org/abs/gr-qc/...
1
vote
1answer
87 views

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 ...
1
vote
0answers
78 views

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. ...
1
vote
0answers
158 views

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,...
1
vote
0answers
140 views

What is the significance of self-duality and anti self-duality in supergravity?

So I see the terms "self-dual" and "anti self-dual" appear routinely in supergravity/string thery, e.g. the fact that Type IIB supergravity contains a real self-dual rank-5 antisymmetric tensor $F_{\...
1
vote
0answers
326 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 ...
0
votes
0answers
28 views

Can the scalar field and time be swapped in Kaluza-klein theory?

In the Kaluza-Klein theory the scalar field was added as a fifth dimension. Was there a specific reason to do that? Could it also be inserted between the three dimensions and time? So, can the scalar ...
0
votes
0answers
42 views

Particle spectrum in dimensional reduction

First of all, sorry if this question is a bit stupid, but my knowledge of certain aspects of particle physics and group theory is a bit limited. I am compactifying the heterotic $E_{8}\times E_{8}$ ...
0
votes
1answer
31 views

What is regular mass spacing?

In a book I'm reading, there is a sentence as follows: Muons and taus are not extra-dimensional versions of electrons, because they don’t have a regular mass spacing and don’t have the same weak-...
0
votes
0answers
198 views

Why is the metric in Kaluza Klein theory set up in the way that it is?

Since the product of the electomagnetic potential with itself and the square of the radion field is added to the 4D space time metric, $$ \left( \begin{array}{ccc} g_{\mu\nu}+A_\mu A_\nu\phi^2 & \...
0
votes
2answers
107 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 ...
0
votes
1answer
85 views

Kaluza suggested metric

Is there a book or a paper that goes into the mathematical details of getting scalar curvature of the 5 dimensional metric that Kaluza wrote down? I am running into many mathematical issues for I am ...