On the Gauge Theory/Geometry Correspondence

TL;DR

This paper explores the duality between SU(N) Chern-Simons theory on S^3 and topological string theory on a conifold geometry, providing exact checks and proposing a derivation from a linear sigma model.

Contribution

It demonstrates an exact duality between Chern-Simons theory and topological strings, with checks at all orders and a new derivation approach from a linear sigma model.

Findings

Exact agreement of partition functions for all mbda

Proposal of a derivation from linear sigma models

Insight into D-brane descriptions from gauge theory phases

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.