Exploring the Dual Low Energy Limits of Superstring Theory

[ShayanJ]

Let's consider superstring theory on a 10 dimensional Minkowski background. And assume there is a D3-brane on which the open strings end and closed strings wander around freely in the background. I want to know, in what limit this gives a supergravity theory in which I can study it by using the brane's SEM tensor in the Einstein's equations to find the curved metric? And in what limit this gives a U(1) gauge theory?(Its easy to say the low energy limit, but how is it that there are two different low energy limits? How are these low energy limits derived from the full theory?)

Thanks

 

[mitchell porter]

I don't really know this stuff, so I don't 100% vouch for the truth of what I'm about to say. But: if you work at energies below the string scale, you can consider just the massless modes of the strings, and you should get an effective theory which is a 10d supergravity coupled to a gauge field localized on a 4d defect in the 10d space-time. Space around the defect is puckered, just like the bowling-ball-on-a-trampoline image of curved space, and if the defect is heavy enough, the "throat" leading down to it is infinitely long. That means the defect becomes invisible to the 10d gravitons - they never reach it and so never interact with it. That is called the decoupling limit - the defect has decoupled from 10d supergravity, the brane has decoupled from the bulk - and in that specific situation, you are left with just the gauge theory. But away from that specific situation, the gauge fields on the brane will remain coupled with the gravitons in the bulk.

 

[ShayanJ]

That much is explained in a lot of books and papers. But I need something more precise and specific.