Chern-Simons Theory and Topological Strings

TL;DR

This paper reviews the connection between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces, highlighting an exact all-orders solution via the topological vertex and its implications for knot theory and geometry.

Contribution

It presents an exact all-orders solution to topological string theory on noncompact Calabi-Yau spaces using the topological vertex, linking gauge theory and string dualities.

Findings

Exact solution of topological string theory via topological vertex

Insights into knot invariants from string/gauge duality

Implications for Calabi-Yau geometry

Abstract

We review the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces. This relation has made possible to give an exact solution of topological string theory on these spaces to all orders in the string coupling constant. We focus on the construction of this solution, which is encoded in the topological vertex, and we emphasize the implications of the physics of string/gauge theory duality for knot theory and for the geometry of Calabi-Yau manifolds.