# Randall Sundrum Model

1. Sep 28, 2005

### robousy

Hi I wanted to ask about the following metric:

$$ds^2=e^{-2 kr_c \: \phi} \: \eta_{\mu \nu} dx^\mu dx^\nu + r_c^2 d\phi^2$$

It is a proposed solution to the hierachy problem i.e the weakness of gravity.

when $$\phi =0$$ the exponential factor goes to 1 and that corresponds to our physical brane, and when it goes to $$\phi = \pi$$ then we have the exponential supression of the spacetime separation and that corresponds to the metric of the hidden brane.

I would like to understand why this has the effect of making gravity weaker.

I have read the paper but don't really understand the physical reasoning.

The paper says 'the weakness of gravity arises because of the small overlap of the graviton wavefunction in the 5th dimension with our brane.'

I don't really get this and would love to hear from someone who understands this.

Looking forward to hearing from someone!

Last edited: Sep 29, 2005
2. Sep 29, 2005

### David

I think we need more information about the model to say anything sensible. What is the reference for this? Giving that metric by itself doesn't indicate a solution to the hierarchy problem in any meaningful way without more information.

3. Sep 29, 2005

Staff Emeritus
In the Randall-Sundrum theory the graviton wave function is produced from rxcitations of a closed string; this is standard string theory. The other bosons are produced from some construction of open strings with their endpoints fixed on branes. Again this is a standard approach. Randall-Sundrum assumes the the branes are, or are within, our four dimensional universe, which is the boundary of a five dimensional brane. Thus the graviton's string can move into the fifth dimension, while the other bosons' strings cannot. Quantally, this means the graviton wave function is at least partially in the higher space, which boils down to less probability of finding the boson in our universe, which translates into a weaker force.

4. Sep 29, 2005

### robousy

Yes, sorry I should have provided the paper reference:

http://arxiv.org/abs/hep-ph/9905221

5. Sep 29, 2005

### robousy

Thanks for your response.

I think my mental picture may be incorrect here.

I was picturing two x (3d+1) branes separated by the extra (compact) dimension in which only gravity can propogate. Is this the right mental picture?

Also, I find the warp factor quite interesting. The extra dimension takes the form $$S_1 \times Z_2$$.

Now, this means the warp factor goes to 1 when $$\phi$$ is zero which is supposed to correspond to the hidden brane and on the 'other side' of the 5th dimension $$\phi$$ goes to $$\pi$$ and the warp factor becomes (very) significant as the $$kr_c$$ is said to be about 50 so we get something on the order of $$e^{-150}$$ and this corresponds to 'our' universe.

Now, the metric is the separation between 2 points - so the warp factor physically translates to space being 'smaller' or 'crunched up' in one universe compared to the other (I think) and I wander if this has any bearing on the picture?

Maybe you help me obtain some insight here?

Thanks!

Last edited: Sep 29, 2005
6. Oct 4, 2005

### robousy

anyone else maybe???

:)