Web Construction of ABCDEFG and Affine Quiver Gauge Theories

Abstract

The topological vertex formalism for 5d $\mathcal{N}=1$ gauge theories is not only a convenient tool to compute the instanton partition function of these theories, but it is also accompanied by a nice algebraic structure that reveals various kinds of nice properties such as dualities and integrability of the underlying theories. The usual refined topological vertex formalism is derived for gauge theories with $A$-type quiver structure (and $A$-type gauge groups). In this article, we propose a construction with a web of vertex operators for all $ABCDEFG$-type and affine quivers by introducing several new vertices into the formalism, based on the reproducing of known instanton partition functions and qq-characters for these theories.

39+21 pages

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Cited by in corpus (13)

• A slow review of the AGT correspondence
• Quantum toroidal algebras and solvable structures in gauge/string theory
• More on topological vertex formalism for 5-brane webs with O5-plane
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Refined topological vertex with ON-planes
• ABCD of qq-characters
• Topological Vertex/anti-Vertex and Supergroup Gauge Theory
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• Quantum $W_{1+\infty }$ subalgebras of BCD type and symmetric polynomials
• Intertwining operator and integrable hierarchies from topological strings