By Minxin Huang

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However, at finite N and gs this is not a duality per say, since we do not have any other nonperturbative definition of type IIB string theory on AdS5 × S 5 . On the other hand, if we take N to be large, then something very fantastic happens. A miraculous but not quite well understood “duality transition” occur at large N, and we could have a dual description of string theory such as classical supergravity. This transition is in some sense like a geometric transition [25]. Let us discuss in what regime the string theory can be approximated by classical supergravity.

Many correlation functions of BPS operators has also been computed and shown to be not dependent on the gauge coupling. We can compare these quantities to the computation from classical supergravity side. Many successful tests have been done in these cases. For review see [11, 12]. 2 Plane Waves and BMN Operators Until recently, most tests of the AdS/CFT correspondence have been restricted to the classical supergravity regime. Can we go beyond classical supergravity to study stringy modes of theory, or even interacting string theory?

We find m1,2 ∼ ±ia and m3 ∼ − Λa 2 For m1,2 we get P4 (x) → x3 (x − 2Λ2 ), a which is a singular limit unless p = 2, in which case the gauge group breaks into U(4) → U(1) × U(3). For m3 we have P4 (x) → 2 x3 (x − Λa ), which is a singular limit unless p = 2, in which case the gauge group breaks into U(4) → U(1) × U(3). 48 Something interesting has happened here. To determine classical limits, we take a point on the factorization locus (parameterized by a and m) and then determine the superpotential which would yield that point as its minimum.