Stringy Instanton Counting and Topological Strings

TL;DR

This paper investigates the stringy instanton partition function in 4D N=2 supersymmetric gauge theories, revealing its relation to K-theoretic and refined topological string partition functions, and explores quantum corrections beyond topological string predictions.

Contribution

It establishes a connection between stringy instanton partition functions and refined topological strings, including analysis of quantum stringy corrections not captured by existing models.

Findings

Relation between stringy instanton and K-theoretic partition functions

Identification of quantum stringy corrections beyond topological string predictions

Insights into geometric engineering of gauge theories

Abstract

We study the stringy instanton partition function of four dimensional ${\cal N}=2$ $U(N)$ supersymmetric gauge theory which was obtained by Bonelli et al in 2013. In type IIB string theory on $\mathbb{C}^2\times T^*\mathbb{P}^1\times \mathbb{C}$, the stringy $U(N)$ instantons of charge $k$ are described by $k$ D1-branes wrapping around the $\mathbb{P}^1$ bound to $N$ D5-branes on $\mathbb{C}^2\times \mathbb{P}^1$. The KK corrections induced by compactification of the $\mathbb{P}^1$ give the stringy corrections. We find a relation between the stringy instanton partition function whose quantum stringy corrections have been removed and the K-theoretic instanton partition function, or by geometric engineering, the refined topological A-model partition function on a local toric Calabi-Yau threefold. We also study the quantum stringy corrections in the stringy instanton partition function which is not captured by the refined topological strings.