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 S${}^1$, 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.

v1: 32 pages, 12 figures, v2: published version

References in corpus (23)

• The Topological Vertex
• The Refined Topological Vertex
• Webs of five-branes and N=2 superconformal field theories
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• ABCD of instantons
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• Non-Lagrangian Theories from Brane Junctions
• Issues on Orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry
• Topological strings and 5d T_N partition functions
• Discrete theta and the 5d superconformal index
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Topological vertex formalism with O5-plane
• Instanton counting and O-vertex
• More on topological vertex formalism for 5-brane webs with O5-plane
• Topological vertex for 6d SCFTs with ${\mathbb{Z}}_2$-twist
• Surface defects on E-string from 5-brane webs
• Refined topological vertex with ON-planes
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• ABCD of qq-characters
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• S-foldings of 5d SCFTs
• Defects and type D relativistic Toda lattice for some 5d gauge theories

Cited by in corpus (1)

• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations