Instantons on Young diagrams with matters

TL;DR

This paper computes unrefined instanton partition functions for 5d gauge theories with matter in non-fundamental representations, verifying theoretical identities via explicit Young diagram sums.

Contribution

It provides explicit formulas for instanton partition functions with matter beyond the fundamental, enabling verification of theoretical identities.

Findings

Confirmed identities among instanton partition functions predicted by Higgsing.

Derived explicit sums over Young diagrams for various 5d gauge theories with matter.

Validated representation theory predictions through these explicit calculations.

Abstract

We present the unrefined instanton partition functions of various 5d gauge theories with matter beyond the fundamental representation as sums over Young diagrams. By using these explicit expressions, we verify a range of identities among the instanton partition functions predicted by Higgsing procedures of fivebrane web diagrams and representation theory.