O-vertex, O7+-plane, and topological vertex

Abstract

We revisit the instanton partition function for 5d $\mathcal{N}$ = 1 SO(N) gauge theories compactified on S¹, computed from the topological vertex formalism with the O-vertex based on a 5-brane web diagram with an O5-plane. We introduce an identity that enables us to rewrite the unrefined partition function into a new expression in terms of the Nekrasov factors summed over Young diagrams, which can be interpreted as the freezing of an O7-plane. Based on this, we propose topological vertex formalism with an O7⁺-plane.