$n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$

Abstract

We propose, following the AGT correspondence, how the ${\mathcal{W}}_{N,n}^{para}$ ($n$-th parafermion ${\mathcal{W}}_N$) minimal model characters are obtained from the $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$ with $\Omega$-deformation by imposing specific conditions which remove the minimal model null states.

arXiv comment25 pages, 2 figures; v2: minor changes, references added; I would like to dedicate this paper to the memory of Professor Omar Foda

References in corpus (23)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• A Strong Coupling Test of S-Duality
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
• Multi instanton calculus on ALE spaces
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• On the instantons and the hypermultiplet mass of N=2* super Yang-Mills on S^4
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Instanton moduli spaces and bases in coset conformal field theory
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• Instantons and 2d Superconformal field theory
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Ramond sector of super Liouville theory from instantons on an ALE space
• Parafermionic Liouville field theory and instantons on ALE spaces
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• AGT, Burge pairs and minimal models
• A Burge tree of Virasoro-type polynomial identities
• Conformal blocks of W_N Minimal Models and AGT correspondence
• AGT, N-Burge partitions and W_N minimal models
• Coset conformal field theory and instanton counting on C^2/Z_p
• N=1 superconformal blocks with Ramond fields from AGT correspondence
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$

Cited by in corpus (4)

• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• The Grassmannian VOA
• Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy