Deriving an action from a metric

[Safinaz]

TL;DR Summary

I try to find out how in this paper https://arxiv.org/abs/hep-ph/9905221
the authors drived an effective action from the metric.

Hello!

The paper I study is related to string theory and modified gravity theories topics.

As they say in page 5 “The four-dimensional effective theory now follows by substituting Eq. (13) into the original action, Eq. (4)”

I wonder how did they drive a 4- dimensional effective metric, equation (13) ?

Then how they did substitute into the higher dimensional action to get the 4- dimensional effective one ?

I have spent many times now reading lecture notes and string theory books to find out what's going on but nothing helpful till now!

So any help is appricated!

 

[LightHero]

The paper you are studying likely explains how they got equation (13) in more detail. You may need to look back at earlier sections and equations in the paper to find out how they arrived at equation (13). It could also be possible that equation (13) was derived in an earlier paper or book and the authors of your paper are just referencing it. If that's the case, you will need to track down the earlier publication to learn more about how equation (13) was derived. Additionally, you could reach out to the authors of the paper directly if you have questions about their research that aren't answered in the paper itself.