# The difference between The Dilaton and The Radion?

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I have read this question on the Dilaton, but I am a little confused with the distinction between the Dilaton and the Radion.

I definitely have the feeling that these two scalar fields are different particles.

I am fimiliar with the Diliton being related to the coupling constant in String Perturbation Theory.

$$g_s = e^{\langle \phi\rangle}$$

Moreover, the Dilaton is related to the size of a compactificated dimension. This was covered in our Bosonic String Theory lectures (I cannot link from outside the network).

On the other hand, the Radion is usually the name given to the $g_{55}$ (or $g_{zz}$ in the notes referenced) component of the metric tensor in a Kaluza-Klein theory, and too is related to the size of the compactified dimension

$$\hat{g}_{zz} = \exp(2 \beta \phi)$$

giving a four-dimensional effective field theory

$$\mathcal{L} = \sqrt{-\hat{g}}\hat{\mathcal{R}} = \sqrt{-g}\left(\mathcal{R} - \frac{1}{2}(\partial \phi)^2 \frac{-1}{4} \exp \left(-2 (D-1) \alpha \phi \right) \mathcal{F}^2 \right)$$

Furthermore, in Randal-Sundrum model I have seen the scalar field called a Radion, even though here we explicitly avoid compactification.

Finally, in the Cyclic Model of the Universe I have heard the moduli scalar field which 'measures' the distance of seperation between the two branes the Radion.

I have been studying the original paper on the Alternative to Compactification and a review on the Cyclic Model of the universe, as well the lecture notes on Kaluza-Klein Theory by C. Pope to try to learn about these things.

User1504 mentions that they are the same in M-Theory and Type IIA string theory, but I am afraid that I have not studied Superstring theory or beyone yet.

So to reiterate, my question is, can anyone give me a discription of the difference between the Dilaton and the Radion?

This post imported from StackExchange Physics at 2014-04-15 05:21 (UCT), posted by SE-user Flint72

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The Dilaton, more commonly called the Radion, in Kaluza -Klein theory is similar to the Dilaton in String Theory. In the Type IIA Superstring Theory, for example, the Dilaton Field, together with the Metric Tensor and the Neveu-Schwarz B-field (analogous to the Electromagnetic Field), can be found in the Neveu-Schwarz Neveu-Schwarz sector.

It is important to notice this, that the graviton, the "photon", and the dilaton are all found in the same sector of Type IIA string theory. The NS-NS sector of the Type IIA superstring theory is actually the sector that gives rise to the Kaluza-Klein theory.

answered Apr 15, 2014 by (1,975 points)

This whole thread makes me feel pinged, even though I have no yellow dot in my inbox :-). I never encountered before that the $g_{55}$ in KK theory is called a radion ...

The Kaluza-Klein scalar field is usually called a radion; the term dilaton is more common in string theory etc. Actually the only use of the word "dilaton" in Kaluza-Klein that I remember is in the "also known as" brackets : )

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