Instanton Counting and Dielectric Branes

TL;DR

This paper demonstrates how Euclidean D0-branes in a specific brane setup reproduce Nekrasov's instanton partition functions for 4D N=2 supersymmetric Yang-Mills theories, highlighting the role of the Myers effect.

Contribution

It establishes a direct link between brane configurations with RR flux and Nekrasov's instanton counting, extending to theories with fundamental hypermultiplets.

Findings

Partition function of D0-branes matches Nekrasov's instanton partition function.

Myers effect is essential in the brane analysis.

Method applies to theories with hypermultiplets in fundamental representation.

Abstract

We consider the Hanany-Witten type brane configuration in a background of RR 4-form field strength and examine the behavior of Euclidean D0-branes propagating between two NS5-branes. We evaluate the partition function of the D0-branes and show that it coincides with the Nekrasov partition function of instantons for four-dimensional N=2 supersymmetric Yang-Mills theory. In this analysis, the Myers effect plays a crucial role. We apply the same method to the brane configuration realizing four-dimensional N=2 theory with hypermultiplets in the fundamental representation and reproduce the corresponding Nekrasov partition function.