Double genus expansion for general Ω background

Abstract

We will show how the refined holomorphic anomaly equation obeyed by the Nekrasov partition function at generic [Formula: see text], [Formula: see text] values becomes compatible, in a certain two-parameter expansion, with the assumption that both parameters are associated to genus counting. The underlying worldsheet theory will be analyzed and constrained in various ways, and we will provide both physical interpretation and some alternative evidence for this model. Finally, we will use the Gopakumar–Vafa formulation for the refined topological string in order to give a more quantitative description.