On the Gauge Theory/Geometry Correspondence
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 1998
- DOI:
- 10.48550/arXiv.hep-th/9811131
- arXiv:
- arXiv:hep-th/9811131
- Bibcode:
- 1998hep.th...11131G
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- 23 pages, harvmac (b)