Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes

TL;DR

This paper links geometric transitions in Calabi-Yau manifolds to Chern-Simons theory and Veneziano amplitudes, providing a new operator method for computing topological string amplitudes.

Contribution

It introduces an operator technique in 2D CFT that simplifies the calculation of all-genus topological string amplitudes for toric Calabi-Yau manifolds.

Findings

Topological string amplitudes expressed as vacuum expectation values of vertex operators.

Amplitudes resemble Veneziano amplitudes from dual resonance models.

Operator method simplifies computations significantly.

Abstract

We consider the geometric transition and compute the all-genus topological string amplitudes expressed in terms of Hopf link invariants and topological vertices of Chern-Simons gauge theory. We introduce an operator technique of 2-dimensional CFT which greatly simplifies the computations. We in particular show that in the case of local Calabi-Yau manifolds described by toric geometry basic amplitudes are written as vacuum expectation values of a product vertex operators and thus appear quite similar to the Veneziano amplitudes of the old dual resonance models. Topological string amplitudes can be easily evaluated using vertex operator algebra.