Understanding AdS/CFT Conjecture: N=4 SYM and D-Brane Dynamics Explained

[nonplus]

Hi!
I am a bit confused about the AdS/CFT conjecture...

One of the things I don't really understand is when N=4 SYM is a valid
description of the D-brane dynamics. My impression was this:
In the open string picture of branes, the massless excitations of the open string connected to the brane leads to the SYM. But at high energy, massive excitations will appear and the SYM will no longer give a complete description, i.e. the field theory limit is no longer valid.

However, when I read superficially through the AdS/CFT-literature, the argument goes that for D3-branes, the SYM is superconformal and therefore a valid description of the brane at any energy.

Is this somehow related to the near-horizon limit?


Any answers would be greatly appreciated!

 

[lumidek]

Ignoring string excitations in AdS/CFT

Hi! For a description of the full physics of D3-branes, the gauge theory is only valid at energies much lower than the string scale. If you want to know everything about D3-branes as embedded in the Minkowski space, you need the excited open string modes and their interactions, too.

In the AdS/CFT correspondence, however, the lower energies you have, the lower you are to the horizon, interior of the black hole. If you only take the low-energy limit of the open string theory living on the D3-branes, you obtain a pure superconformal gauge theory.

It is the same limit that, in the closed string or gravity description, corresponds to the near-horizon geometry of the black 3-brane geometry. Ignoring the excited string modes is thus equivalent to ignoring the Minkowski "end" of the geometry, and only considering the near-horizon geometry. This equivalence between the AdS5 x S5 (not to be confused with the full asymptotically Minkowski geometry around 3-branes) and the pure gauge theory is exact.

Best
Lubos, http://motls.blogspot.com/

 

[nonplus]

Hi! For a description of the full physics of D3-branes, the gauge theory is only valid at energies much lower than the string scale. If you want to know everything about D3-branes as embedded in the Minkowski space, you need the excited open string modes and their interactions, too.

In the AdS/CFT correspondence, however, the lower energies you have, the lower you are to the horizon, interior of the black hole. If you only take the low-energy limit of the open string theory living on the D3-branes, you obtain a pure superconformal gauge theory.

It is the same limit that, in the closed string or gravity description, corresponds to the near-horizon geometry of the black 3-brane geometry. Ignoring the excited string modes is thus equivalent to ignoring the Minkowski "end" of the geometry, and only considering the near-horizon geometry. This equivalence between the AdS5 x S5 (not to be confused with the full asymptotically Minkowski geometry around 3-branes) and the pure gauge theory is exact.

Best
Lubos, http://motls.blogspot.com/

I see, thank you!
I feel somehow less confused...

nonplus