All Loop Topological String Amplitudes From Chern-Simons Theory

TL;DR

This paper establishes a deep connection between topological string amplitudes on toric Calabi-Yau threefolds and knot invariants from Chern-Simons theory, enabling high-degree computations and revealing new large N dualities.

Contribution

It proves the equivalence of topological string amplitudes with Chern-Simons knot invariants and computes these amplitudes explicitly for specific geometries to all genera.

Findings

Computed topological string amplitudes for P2 up to degree 12 and P1 x P1 up to degree 10 to all genera.

Established new large N dualities involving type II superstrings on local Calabi-Yau threefolds.

Demonstrated the use of Chern-Simons theory to efficiently calculate string amplitudes.

Abstract

We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In particular we explicitly compute the topological string amplitudes for P2 up to degree 12 and P1 x P1 up to total degree 10 to all genera. This also leads to certain novel large N dualities in the context of ordinary superstrings, involving duals of type II superstrings on local Calabi-Yau three-folds without any fluxes.