Instanton counting and O-vertex

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.

14+17 pages; a mathematica file that can help the readers to check our results is attached; typos corrected in v5

References in corpus (8)

• The Refined Topological Vertex
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Instantons from Blow-up
• More on topological vertex formalism for 5-brane webs with O5-plane
• On the Jeffrey-Kirwan residue of BCD-instantons
• Instantons to the people: the power of one-form symmetries
• Recursive Method for Nekrasov partition function for classical Lie groups

Cited by in corpus (14)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• Refined topological vertex with ON-planes
• ABCD of qq-characters
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• $DE$-type little strings from glued brane webs
• Instantons on Young diagrams with matters
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• New dimer integrable systems and defects in five dimensional gauge theory
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• Defects and type D relativistic Toda lattice for some 5d gauge theories
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations