Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I

TL;DR

This paper uses instanton counting to derive the Seiberg-Witten geometry for a class of four-dimensional N=2 supersymmetric quiver gauge theories with alternating SO and USp groups, confirming previous string theory results.

Contribution

It introduces a novel application of instanton counting and saddle point analysis to determine Seiberg-Witten geometry for SO-USp quivers, providing explicit solutions and matching known string theory solutions.

Findings

Derived limit shape equations for instanton configurations.

Explicit Seiberg-Witten geometry for linear quiver theories.

Confirmed agreement with string theory brane construction results.

Abstract

We apply the instanton counting method to study a class of four-dimensional $\mathcal{N}=2$ supersymmetric quiver gauge theories with alternating $\mathrm{SO}$ and $\mathrm{USp}$ gauge groups. We compute the partition function in the $\Omega$-background and express it as functional integrals over density functions. Applying the saddle point method, we derive the limit shape equations which determine the dominant instanton configurations in the flat space limit. The solution to the limit shape equations gives the Seiberg-Witten geometry of the low energy effective theory. As an illustrating example, we work out explicitly the Seiberg-Witten geometry for linear quiver gauge theories. Our result matches the Seiberg-Witten solution obtained previously using the method of brane constructions in string theory.