Wall-crossing between stable and co-stable ADHM data

TL;DR

This paper proves a formula relating Nekrasov partition functions derived from stable and co-stable ADHM data on the plane, using wall-crossing techniques, and connects to conjectures for $A_{1}$ singularity.

Contribution

It establishes a new wall-crossing formula between stable and co-stable ADHM data, extending the understanding of Nekrasov partition functions.

Findings

Proves a formula linking stable and co-stable Nekrasov partition functions.

Uses Nakajima-Yoshioka's method and Mochizuki's wall-crossing theory.

Connects to conjectures for $A_{1}$ singularity.

Abstract

We prove formula between Nekrasov partition functions defined from stable and co-stable ADHM data for the plane following method by Nakajima-Yoshioka based on the theory of wall-crossing formula developed by Mochizuki. This formula is similar to conjectures by Itoh-Maruyoshi-Okuda for $A_{1}$ singularity.