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arXiv · hep-th/9811131

On the Gauge Theory/Geometry Correspondence

Rajesh Gopakumar·Cumrun Vafa
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Abstract

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 $B$-field on the $S^2$ has magnitude $Ng_s=λ$, 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.

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Rajesh Gopakumar, Cumrun Vafa. 1998-11-13. On the Gauge Theory/Geometry Correspondence. https://arxiv.org/abs/hep-th/9811131

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