1998/11/13 by Rajesh Gopakumar, Cumrun Vafa · 6 citations
Physics and Astronomy · #hep-th
published as Adv.Theor.Math.Phys. 3 (1999) 1415-1443 · 23 pages, harvmac (b)
arxiv created 1998/11/13 · arxiv updated 2009/11/30
The 't Hooft expansion of SU(N) Chern-Simons theory on S3 is proposed to be exactly dual to the topological closed string theory on the S2 blow up of the conifold geometry. The B-field on the S2 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 \it 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.