On the Gauge Theory/Geometry Correspondence

The ’t Hooft expansion of SU(N) Chern-Simons theory on S is proposed to be exactly dual to the topological closed string theory on the S blow up of the conifold geometry. The B-field on the S has magnitude Ngs = λ, 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 λ and to all orders in 1/N . Moreover, 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(1) gauge theory. This approach holds promise for a derivation of the AdS/CFT correspondence.