Localization and Gluing of Topological Amplitudes

TL;DR

This paper introduces a new algorithm for computing Gromov-Witten invariants of toric Calabi-Yau threefolds using localization and graph-based gluing, linking generating functions of Hodge integrals to the topological vertex.

Contribution

It presents a novel gluing algorithm for topological amplitudes that connects Hodge integrals with the topological vertex at fractional framing.

Findings

Developed a gluing algorithm based on localization and graphs.

Established a conjectural relation between Hodge integrals and the topological vertex.

Provided a new computational approach for topological string amplitudes.

Abstract

We develop a gluing algorithm for Gromov-Witten invariants of toric Calabi-Yau threefolds based on localization and gluing graphs. The main building block of this algorithm is a generating function of cubic Hodge integrals of special form. We conjecture a precise relation between this generating function and the topological vertex at fractional framing.