On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories

TL;DR

This paper explores the connection between integrable structures in supersymmetric gauge theories and refined topological string theory, revealing a geometric transition that links open and closed string partition functions.

Contribution

It generalizes a known field theoretic correspondence within the refined topological string framework, demonstrating it as a special limit of the refined geometric transition.

Findings

Explicit realization of the correspondence via open-closed geometric transition

Recasting the integrable structure correspondence as a geometric transition

Embedding the gauge theory correspondence into refined topological string theory

Abstract

We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field theories can be recast as a special limit of the refined geometric transition relating open and closed topological string partition functions. We realize the simplest examples of the correspondence explicitly in terms of open-closed geometric transition.