I am a bit confused about Maldacena's original decoupling argument. There are two different low energy (i.e, α′→0) descriptions of the stack of D3-branes:
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N=4 SYM and 10D type IIB SUGRA.
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Full type IIB superstring in AdS5×S5 and 10D type IIB SUGRA.
Comparing (1) and (2) (actually cancelling 10D SUGRA!) we obtain the celebrated AdS/CFT correspondence. I have the following questions regarding this argument.
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If one takes α′→0 it is same as taking GN→0. Then how do the branes backreact to produce non-trivial background namely AdS5×S5?
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One arrives at the AdS/CFT correspondence by taking α′→0, by the above decoupling argument. Then how can one claim that there should be full string theory in AdS5×S5? I understand that any high-energy excitation will be infinitely red-shifted for the observer at infinity. But these are all happening at α′→0!
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Isn't full string theory defined only on asymptotically AdS rather than AdS? (I am not sure about this though.)
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Also the radius of the S5 turns out to be same as AdS5 scale, L. Now small L means highly fluctuating string i.e., quantum gravity regime and thus notion of this classical backgrounds break down. Then how can one do Kaluza-Klein reduction of the S5 ?
This post imported from StackExchange Physics at 2015-07-26 09:29 (UTC), posted by SE-user pinu