Instanton counting and O-vertex

TL;DR

This paper derives explicit formulas for unrefined instanton partition functions of BCD-type gauge groups using Young diagrams and introduces a new O-vertex in the topological vertex formalism to represent O5-planes.

Contribution

It provides the first closed-form expressions for these instanton partition functions and extends the topological vertex formalism with a novel O-vertex for O5-planes.

Findings

Explicit formulas for BCD gauge group instanton partition functions.

Introduction of O-vertex in topological vertex formalism.

Connection between fivebrane webs and instanton counting.

Abstract

We present closed-form expressions of unrefined instanton partition functions for gauge groups of type $BCD$ as sums over Young diagrams. For $\mathrm{SO}(n)$ gauge groups, we provide a fivebrane web picture of our formula based on the vertex-operator formalism of the topological vertex with a new type called O-vertex for an O5-plane.