The 't Hooft expansion of SU(N) Chern-Simons theory on S'3 is proposed to be exactly dual to the topological closed string theory on the S 2 blow up of the conifold geometry. The Bfield on the S 2 has magnitude iV^ = A, the 't Hooft coupling. We are able to make a number of checks, such as finding exact agreement at the level of the partition function computed on both sides for arbitrary A and to all orders in 1/7V. Moreover, e-print archive: http://xxx.lanLgov/hep-th/9811131 1416 R. GOPAKUMAR AND C. VAFA it seems possible to derive this correspondence from a linear sigma model description of the conifold. We propose a picture whereby a perturbative D-brane description, in terms of holes in the closed string worldsheet, arises automatically from the coexistence of two phases in the underlying U(l) gauge theory. This approach holds promise for a derivation of the AdS/CFT correspondence.

We propose a duality between the 2d W N minimal models in the large N 't Hooft limit, and a family of higher spin theories on AdS 3 . The 2d CFTs can be described as WZW coset models, and include, for N = 2, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the RG flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an AdS 4 dual for the singlet sector of large N vector models.

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It is conjectured that strongly coupled, spatially noncommutative N = 4 Yang-Mills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for