Chern-Simons Theory, Holography and Topological Strings

TL;DR

This paper reviews the connections between Chern-Simons theory, topological strings, and holography, highlighting dualities, computations of string amplitudes, and applications to link invariants and black hole physics.

Contribution

It clarifies the duality between the Kahler form and gauge field strength, and explains how to compute topological string amplitudes using the topological vertex.

Findings

Demonstrates the duality between Kahler form and 3-form gauge potential.

Shows how to compute topological string amplitudes via topological vertex.

Reviews applications to link invariants and black hole physics.

Abstract

In this note we present a brief overview of connections between Chern-Simons theory and topological strings. A prominent role in this link has been played by large N dualities and holography. We demystify this by explaining why the Kahler form should be viewed as dual to the field strength associated with a 3-form gauge potential, sourced by Lagrangian D-branes. We explain how this leads to the computation of topological string amplitudes in terms of topological vertex for toric Calabi-Yau threefolds. Furthermore, applications of topological strings to a conceptual derivation of Skein relations for link invariants as well as some of its physical applications to black hole physics are also reviewed.