On the gauge theory/geometry correspondence

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,