The ABCDEFG of Instantons and W-algebras

Abstract

For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N=2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.

30 pages, 2 figures, v4: a reference added

References in corpus (3)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• From SO/Sp instantons to W-algebra blocks
• Towards a 4d/2d correspondence for Sicilian quivers

Cited by in corpus (58)

• Non-Lagrangian Theories from Brane Junctions
• Coulomb Branch and The Moduli Space of Instantons
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Universal Features of BPS Strings in Six-dimensional SCFTs
• $(0,4)$ dualities
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Hilbert Series for Moduli Spaces of Two Instantons
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Counting Exceptional Instantons
• 2d TQFT structure of the superconformal indices with outer-automorphism twists
• On Exceptional Instanton Strings
• W_3 irregular states and isolated N=2 superconformal field theories
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• A "Lagrangian" for the E7 Superconformal Theory
• A slow review of the AGT correspondence
• New N=1 Dualities from M5-branes and Outer-automorphism Twists
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• ADE Spectral Networks
• Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories
• On the 5d instanton index as a Hilbert series
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Compactification on the Ω-background and the AGT correspondence
• Instantons from Blow-up
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Higgs, Coulomb, and Hall-Littlewood
• Quantum toroidal algebras and solvable structures in gauge/string theory
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Instanton counting and O-vertex
• More on topological vertex formalism for 5-brane webs with O5-plane
• Vortex counting from field theory
• A geometric recipe for twisted superpotentials
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• On the Jeffrey-Kirwan residue of BCD-instantons
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Partition functions of web diagrams with an O7${}^{-}$-plane
• Construction and Deconstruction of Single Instanton Hilbert Series
• Twisted 6d $(2,0)$ SCFTs on a Circle
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Instantons to the people: the power of one-form symmetries
• Recursive Method for Nekrasov partition function for classical Lie groups
• ABCD of 't Hooft operators
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Little String Origin of Surface Defects
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• More on Affine Dynkin Quiver Yangians
• Refined topological vertex for a 5D $Sp(N)$ gauge theory with antisymmetric matter
• Describing codimension two defects
• Five-dimensional gauge theories and the local B-model
• Integrals of motion in conformal field theory with W-symmetry and the ODE/IM correspondence
• Aspects of the moduli space of instantons on $\mathbb{C}{P}^2$ and its orbifolds
• Affine characters at negative level and elliptic genera of non-critical strings
• Integrals of motion in $W{E}_6$ CFT and the ODE/IM correspondence
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries