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On the Gauge Theory/Geometry Correspondence

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arxiv hep-th/9811131 v1 pith:JKMEJVU7 submitted 1998-11-13 hep-th

Rajesh Gopakumar , Cumrun Vafa This is my paper · ORCID
classification hep-th
keywords theorycorrespondenceclosedconifolddescriptiongaugegeometryhooft
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $Ng_s=\lambda$, 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 $\lambda$ 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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Cited by 12 Pith papers

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