All Genus Topological String Amplitudes and 5-brane Webs as Feynman Diagrams

TL;DR

This paper proposes a novel method to compute all genus topological string amplitudes on toric Calabi-Yau threefolds by interpreting 5-brane webs as Feynman diagrams, verified through explicit calculations.

Contribution

It introduces a Feynman diagram approach to topological string amplitudes using 5-brane webs, providing a new computational framework and verifying it with explicit examples.

Findings

The conjecture that 5-brane web amplitudes equal closed string partition functions is supported.

Explicit calculations match known invariants for the resolved conifold.

The method applies to various local Calabi-Yau geometries.

Abstract

A conjecture for computing all genus topological closed string amplitudes on toric local Calabi-Yau threefolds, by interpreting the associated 5-brane web as a Feynman diagram, is given. A propagator and a three point vertex is defined which allows us to write down the amplitude associated with 5-brane web. We verify the conjecture that this amplitude is equal to the closed string partition function by computing integer invariants for resolved conifold and certain curves of low degree in local del Pezzo surfaces, local Hirzebruch surfaces and their various blowups.