SU(N) Geometries and Topological String Amplitudes

TL;DR

This paper verifies a conjecture that topological string partition functions for certain CY3-folds related to SU(N) gauge theories can be derived from gauge instanton calculus, using diagrammatic techniques and Gopakumar-Vafa invariants.

Contribution

It provides a verification of the conjecture by calculating partition functions and Gopakumar-Vafa invariants for CY3-folds associated with SU(N) gauge theories.

Findings

Partition functions match gauge instanton calculations

Gopakumar-Vafa invariants determined to all orders

Field theory limit successfully obtained

Abstract

It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3-folds giving rise to N=2 4D SU(N) gauge theory via geometric engineering can be obtained from gauge instanton calculus. We verify this surprising conjecture by calculating the partition functions for such local CYs using diagrammatic techniques inspired by geometric transitions. Determining the Gopakumar-Vafa invariants for these geometries to all orders in the fiber wrappings allows us to take the field theory limit.