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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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Why Dirac's spin-$\frac12$ theory proves wrong Kaluza-Klein theory?

I recently saw Sabine's short video that mentions that Dirac's spin-$\frac12$ theory proves wrong Kaluza-Klein theory unless supersymmetry is amended to the Kaluza-Klein. Is there a more detailed ...
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Approximation of solution for Laplace's equation in 5d (Kaluza-Klein)

I apologize for the following question because it will seem like a cheap please help me with my homework one. I just want a hint as to what direction to follow. Suppose we have a 5d space where the ...
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Gauge transformation and Kaluza-Klein metric

The Kaluza-Klein metric, by reduction, can be written as a $(4+m) \times (4+m)$ symmetric matrix, where $m$ is the dimension of the additional spacetime (if we decompose $M_D = M_4 \times M_m$). It ...
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Scalar spherical harmonics in $S_n$

In the Kaluza klein reduction we can "decompose" the spacetime $M_n$ as $M_n = M_4 \otimes K_d$, in which $K_d$ is a compact spacetime. So, functions like a scalar $\phi(x,y)$ can be ...
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Is the Kalb-Ramond $B_{\mu\nu}$ equivalent to Kaluza-Klein $A_\mu$?

The low-energy effective action of the bosonic string in the critical dimension $D=26$ can be written as: $$S=\frac{1}{2\kappa_0^2}\int d^{26}x\sqrt{-G} \left[ \phi^2\left( R-\frac{1}{12}H_{\mu\nu\...
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Raising a solution to 4D after having dimensionally reduced it

I am applying the method that Gibbons presents in this article, and it consists of dimensionally reducing a four-dimensional Lagrangian using Kaluza Klein in $S_1$, to a three-dimensional one and ...
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Electromagnetic interaction of a scalar field before KK reduction

Consider the following gravitational action in $d+1$ accompanied with a complex scalar field $\chi$ with a mass $m$: $$S=\int d^{d+1}x\sqrt{-\tilde{g}}\left[\tilde{R}+\tilde{g}^{\mu\nu}\partial_{\mu}\...
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$B$-field reducion in the Kaluza-Klein mechanism

Given the following $d+1$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string: $$S=\frac{1}{2\kappa^2}\int d^{d+1}x\sqrt{-\tilde{G}}e^{-2\tilde{\Phi}...
Daniel Vainshtein's user avatar
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Examples of the Kaluza-Klein dimensional reduction method

I am looking for references or articles that apply or explain how to apply the dimensional reduction method to known metrics such as Minkowski, Schwarzschild, Kerr, etc. The references I found ...
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Why do the scalars always occupy the coset they do?

If I reduce a $D$-dimensional theory on a $d$-dimensional manifold $M_d$, then I will be left with some reduced, effectively $(D-d)$-dimensional theory with some global symmetry group $G$. In general, ...
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Do singular $G_2$-holonomy manifolds in M-theory have stable compactifications?

In this paper: Chiral Fermions from Manifolds of G2 Holonomy it is shown that compactifications of M-theory on a $7d$ $G_2$-holonomy manifold $X$, generate chiral fermions, if only $X$ is singular. I ...
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Expansion about a background classical solution to the Kaluza-Klein five-dimensional field equations

This is a paper I am reading Five-dimensional quantum gravity and the residual length by Roberto Balbinot and Antonio Barletta. I am not able to figure out how he got the expressions in equations 2.11-...
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Explanation of Hierarchy Problem in Kaluza-Klein String Scenarios

During the last few days I have been interested in the gravitational hierarchy problem and the different explanations for it/solutions to it. Among the most "concrete" (insofar as anything ...
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Do the "extra dimensions" in string theory have equivalent physical value to regular dimensions?

I've seen hyperspace dimensions being discussed in models for superstring theory, where there are 6-7 hyperspace dimensions iirc. But the explanation as to why we don't perceive these extra dimensions ...
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Why don't the extra compact dimensions collapse on themselves?

Why are the extra compact dimensions stable and do not collapse? I know the anomaly cancellation is the reason why the extra dimensions are necessary. But I can not visulize how the anomaly ...
Bastam Tajik's user avatar
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A way to visualize extra compact dimensions

I'm wondering if it's valid to think of the meaning of compact dimensions in this way: Suppose a world with two dimensions and a potential $V(x,y)=\kappa\delta(y)$ Then solving the Schrodinger ...
Bastam Tajik's user avatar
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Poincare transformation and extra compact dimensions

Given that Poincare transformation can mix different different directions of spacetime with each other, does this mean that in the case that some dimensions are compactified, large and compact ...
Bastam Tajik's user avatar
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Kaluza-Klein reducing the Chern-Simons term in 11D supergravity

In 11D supergravity we have the Chern-Simons term of the 3-form field $C$ \begin{equation} \int C \land d C \land d C \end{equation} I want to consider this on a spacetime $\mathbb{R}^{1,6}\times S$ ...
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Problem in the general Einstein-Hilbert action of non-abelian Kaluza-Klein theory in four dimensions (1+1D, and 2D)

Background I am interested in the computation of the four-dimensional Einstein-Hilbert action seen as the "inverse" of the Kaluza-Klein procedure. That is, I want to write something like: \...
Jeanbaptiste Roux's user avatar
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String Compactification on a Circle Results in a Moduli Space?

I have been reviewing some string theory for a project I'm working on and I have some questions regarding string compactifications on a circle and the precise definition/origin of the moduli space ...
cpollack's user avatar
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Opening a door to another dimension (Kaluza-Klein like model)

I start the subject with a small fantasy tale: You walk in a forest, until you find a door standing on the ground. You open the door, which let you enter a large room. You are surprised since that ...
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Are there examples of harmonic differential forms in non-singular projective algebraic varieties that appear in general relativity or quantum physics?

I would like to study some real physical examples of harmonic differential forms in non-singular projective algebraic varieties. As Calabi - Yau and Kahler manifolds are used in supersymmetry theories ...
Rajaram Venkataramani's user avatar
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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 ...
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Is it possible to treat the time dimension as the rate of change of an extra spatial dimension? [closed]

In Minkowski Spacetime metric the time dimension is multiplied with $c$. This would allow us to swap it against a fourth space dimension: $cdt=dx_4$. One interpretation would be that the rate of ...
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Question about Kaluza-Klein excitations

In Randall Sundrum (RS) model-type 1 : A Large Mass Hierarchy from a Small Extra Dimension, it’s mentioned that: This result contrasts sharply with the scenario of large extra dimensions for solving ...
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Question about dark matter/energy and other dimensions

According to drummer and lyricist Henrik Ohlsson, the title Dark Matter Dimensions refers to the "appreciation and acknowledgement of the unseen worlds and dimensions, because without the ...
Jesse Flynn's user avatar
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Kaluza-Klein dimensional reduction with Kalb-Rammond field present

When looking at sources on KK dimensional reduction, usually only the metric and/or the vielbein are discussed. However, if we have other fields present, especially p-forms, then there arise some ...
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A geometric understanding of Kaluza-Klein theory?

Here's how I understand the Einstein field equations: in the presence of pure mass (no pressure), the eigen-basis of the Ricci tensor is the same as the particle's rest frame, and all 4 components are ...
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Basic confusion about interpretation of the 5th dimension in Kaluza-Klein theory

As has been mentioned in other posts, Kaluza originally didn't require the 5th dimension to be curled up/compactified. So how exactly would our 4D world emerge from a non-compactified 5D manifold? I ...
Adam Herbst's user avatar
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Help with Kaluza-Klein Christoffel symbols

For \begin{align} \tilde{\Gamma}^\lambda_{\mu\nu} & = \frac{1}{2} \tilde{g}^{\lambda X} \left(\partial_\mu \tilde{g}_{\nu X} + \partial_\nu \tilde{g}_{\mu X} - \partial_X \tilde{g}_{\mu\nu}\right) ...
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Kaluza-Klein mechanism reparameterization $A'_\mu=A_\mu-\partial_\mu\lambda$

Polchinski String Theory volume 1 chapter 8 the parameterize of the metric in Kaluza-Klein mechanism was given by $$ds^2 =G_{\mu\nu} dx^\mu dx^\nu + G_{dd}(dx^d +A_\mu dx^\mu)^2$$ where $\mu,\nu\in [...
ShoutOutAndCalculate's user avatar
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Is classical Kaluza Klein theory stable or not?

Set Up In the original classical Kaluza Klein theory, you have a $d+1$ dimensional manifold where one space dimension is a circle $S^1$. In the "low energy limit," none of the metric ...
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How many extra dimensions needed to model the Strong interaction with a Kaluza-Klein extended theory?

The blog / video (See: https://backreaction.blogspot.com/2021/04/does-universe-have-higher-dimensions.html - Does the Universe have Higher Dimensions? Sabine Hossenfelder's blog) is discussing the ...
shm.physics's user avatar
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How and why does toroidal compactification fail to capture observed physics?

My question is motivated by a statement in this chapter (emphasis added, off-topic statements about supersymmetry elided): Compactifying on tori ... is very interesting for its simplicity ... but not ...
biochemist's user avatar
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The action of the Kaluza–Klein reduction (Chapter 4 of "D-branes (Clifford Johnson)")

In the first part of Section 4, the author gives \begin{equation} S = \frac1{16\pi G^N_{(5)}}\int(-G_{(5)})^{1/2}R^{(5)}d^5x = \frac1{16\pi G^N_{(4)}}\int(-G_{(4)})^{1/2}\Big(R^{(4)} - \frac32\...
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3 answers
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Might the Kaluza-Klein scalar provide a solution to the dark puzzles?

Kaluza-Klein theories of a five-dimensional spacetime yield not only the equations of general relativity and electromagnetism, but also a scalar field. This scalar field, sometimes quantised as the ...
Guy Inchbald's user avatar
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Has Kaluza-Klein Theory been quantized, and if so what distinguishes it from QED & EFT Quantum Gravity?

I know some aspects such as the extra dimensions have been used in String Theory, but is it possible to make a Quantum Field Theory out of Kaluza-Klein Theory, and how does it differ from Quantum ...
Thatpotatoisaspy's user avatar
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Why did Kaluza-Klein need an additional dimension? [closed]

Why did Kaluza-Klein need an additional dimension and not just treat the fourth dimension as a description of both time and space? Assume that you can exchange the time dimension to a space dimension ...
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Constructing explicit coordinates on the Romans space $T^{1,1}$

I am trying to understand coordinates on the space $T^{1,1} = SU(2) \times SU(2) / U(1)$, which shows up in applications of AdS/CFT. It was originally introduced by Romans as a compactification of $d=...
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Kaluza-Klein supermultiplet of 11D supergravity

I am studying Adel Belali's review paper "M(atrix) theory: a pedagogical introduction" for my undergraduate thesis. In the third lecture, part one, we dimensionally reduce 11D supergravity ...
saad's user avatar
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Relationship between scaling dimension and mass in AdS/CFT

I've been reading Horatiu Nastase's notes on AdS/CFT, but I was confused about a certain relationship he claimed. If we compactify supergravity on $AdS_5\times S^5$, we may expand the fields in Kaluza-...
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Why does T-duality not create consistent string theories below the critical dimension?

As I know it, T-duality essentially tells us that if we compactify a superstring theory on a circle of radius $R$, it is equivalent to a string theory compactified on a circle of radius $\tfrac{\alpha'...
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Possibility of the existence of Graviphotons?

I have been attempting to do research on the graviphoton yet I can find almost nothing, and many of the articles I do find are locked behind hefty paywalls. It is an interesting possibility to think ...
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Graviton-Dilaton Action for Kaluza-Klein in Polchinski (8.1.9)

Polchinski uses the graviton-dilaton action (8.1.9) in his String Theory book $$S_1= \frac{1}{2\kappa_0^2}\int d^D x\, \sqrt{-G} e^{-2\Phi} \left[ {R} + 4 \nabla_\mu\Phi \nabla^\mu \Phi \right] \tag{...
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Spin connection, curvature

The metric is ($a,b, = 0,1,2,3,4$) \begin{equation}\label{eq:1} ds^2 = g_{\mu\nu}dx^\mu dx^\nu + e^{2\sigma}(dx^4 + A_\mu dx^\mu)^2 = \eta_{ab}e^ae^b + (e^4)^2. \end{equation} The vielbeins are $e^a = ...
KoKo_physmath's user avatar
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Kaluza-Klein metric and Ricci scalar?

The metric is \begin{equation} ds^2 = G^D_{MN}dx^M dx^N = G_{\mu\nu}dx^\mu dx^\nu + G_{dd}(dx^d + A_\mu dx^\mu)^2. \end{equation} Then \begin{equation} G^D = \begin{bmatrix} G_{\mu\nu} + G_{dd}A_\mu ...
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How to explain "compactification of a dimension"

The first paragraph of the wikipedia entry on "compactification (physics)" explains that it "means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with ...
Tommy R. Jensen's user avatar
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Is there an equivalent of Kaluza-Klein for fermionic dimensions?

Taking GR in $D$ dimensions, one can use the process of compactification to turn this into GR in $D-1$ dimensions coupled to a Yang-Mills field. i.e. you start with spin-2 fields and you and up with ...
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Can one derive charged black hole solution of GR using Kaluza-Klein?

Kaluza-Klein showed that a 5 dimensional gravitional theory with one dimension on a circle, is equivalent in the limit to a 4 dimensional gravitational theory with electromagnetism. So for the ...
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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 ...
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