Fermionic gluing principle of the topological vertex

TL;DR

This paper proposes a fermionic gluing principle for the topological vertex, linking Gromov-Witten invariants of toric Calabi-Yau threefolds to Bogoliubov transforms under the framed ADKMV conjecture.

Contribution

It establishes a fermionic gluing principle for the topological vertex assuming the framed ADKMV conjecture, connecting generating functions to Bogoliubov transforms.

Findings

Gromov-Witten invariants are expressed as Bogoliubov transforms.

The fermionic gluing principle is established under the ADKMV conjecture.

Provides a new perspective on topological string theory computations.

Abstract

We will establish the fermionic gluing principle of the topological vertex, that is, provided the framed ADKMV conjecture, the generating functions of the Gromov-Witten invariants of all toric Calabi-Yau threefolds are Bogoliubov transforms of the vacuum.