A Vertex Formalism for Local Ruled Surfaces

TL;DR

This paper introduces a new vertex formalism for calculating topological string amplitudes on ruled surfaces within Calabi-Yau threefolds, leveraging large N duality and localization techniques.

Contribution

It presents a novel vertex formalism applicable to ruled surfaces with reducible fibers, expanding computational tools in topological string theory.

Findings

Formalism effectively computes string amplitudes on complex geometries

Potential for generalization to broader Calabi-Yau classes

Framework based on large N duality and localization

Abstract

We develop a vertex formalism for topological string amplitudes on ruled surfaces with an arbitrary number of reducible fibers embedded in a Calabi-Yau threefold. Our construction is based on large N duality and localization with respect to a degenerate torus action. We also discuss potential generalizations of our formalism to a broader class of Calabi-Yau threefolds using the same underlying principles.