More on topological vertex formalism for 5-brane webs with O5-plane

Abstract

We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of arXiv:1709.01928. Using the O-vertex it is possible to compute the Nekrasov partition functions of 5d theories realized on any 5-brane web diagrams with O5-planes. We apply our proposal to 5-brane webs with an O5-plane and compute the partition functions of pure SO($N$) gauge theories and the pure $G_2$ gauge theory. The obtained results agree with the results known in the literature. We also compute the partition function of the pure SU(3) gauge theory with the Chern-Simons level $9$. At the end we rewrite the O-vertex in a form of a vertex operator.

arXiv comment41+12 pages, minor corrections in v2

References in corpus (63)

• The Topological Vertex
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• The Refined Topological Vertex
• Branes, Superpotentials and Superconformal Fixed Points
• Integrating Over Higgs Branches
• Elliptic genera of 2d N=2 gauge theories
• Webs of five-branes and N=2 superconformal field theories
• Instanton counting on blowup. I. 4-dimensional pure gauge theory
• M-Strings
• On Geometric Classification of 5d SCFTs
• Witten Index and Wall Crossing
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• ABCD of instantons
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• The Hilbert Series of the One Instanton Moduli Space
• Refined Topological Vertex and Instanton Counting
• Four-Dimensional Avatars of Two-Dimensional RCFT
• Crystal Melting and Toric Calabi-Yau Manifolds
• On orbifolds of M-Strings
• Non-Lagrangian Theories from Brane Junctions
• Instanton counting, Macdonald function and the moduli space of D-branes
• Topological strings and 5d T_N partition functions
• Discrete theta and the 5d superconformal index
• Brane webs and $O5$-planes
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• Instantons on Quivers and Orientifolds
• Quiver W-algebras
• Dualities and 5-brane webs for 5d rank 2 SCFTs
• The ABCDEFG of Instantons and W-algebras
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Compactification of 6d minimal SCFTs on Riemann surfaces
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Line defects and 5d instanton partition functions
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Quiver Yangian from Crystal Melting
• Wall Crossing and M-theory
• 5d/6d DE instantons from trivalent gluing of web diagrams
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Counting Exceptional Instantons
• Orientifold planes, affine algebras and magnetic monopoles
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Emergent Calabi-Yau Geometry
• From SO/Sp instantons to W-algebra blocks
• Quiver elliptic W-algebras
• Exact partition functions of Higgsed 5d $T_N$ theories
• Blowup Equations for 6d SCFTs. I
• Blowup Equations for Refined Topological Strings
• Discrete theta angle from an O5-plane
• Topological vertex formalism with O5-plane
• Refined geometric transition and $qq$-characters
• Instantons from Blow-up
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• On the Quantization of Seiberg-Witten Geometry
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings
• Partition functions of web diagrams with an O7${}^{-}$-plane
• An elliptic topological vertex
• Surface defects on E-string from 5-brane webs
• The Splitting of Branes on Orientifold Planes
• Topological Vertex/anti-Vertex and Supergroup Gauge Theory
• Double quantization of Seiberg-Witten geometry and W-algebras

Cited by in corpus (14)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• Instanton counting and O-vertex
• Refined topological vertex with ON-planes
• ABCD of qq-characters
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• 6d/5d exceptional gauge theories from web diagrams
• Instantons on Young diagrams with matters
• $DE$-type little strings from glued brane webs
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations