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