Coset conformal blocks and N=2 gauge theories

Abstract

It was recently suggested that the su(N)_k+su(N)_p/su(N)_{k+p} coset conformal field theories should be related to N=2 SU(N) gauge theories on R^4/Z_p. In this paper we study various aspects of this proposal. We perform explicit checks of the relation for (N,p)=(2,4), where the symmetry algebra of the coset is the so called S_3 parafermion algebra. Even though the symmetry algebra of the coset is unknown for generic (N,p) models, we manage to perform non-trivial checks in the general case by using knowledge of the Kac determinant of the coset CFT. We also find evidence that the conformal blocks of the (N,p) model should factorise into a certain product of p (N,1) conformal blocks. Precisely this structure is present in the instanton partition function on R^4/Z_p.

24 pages

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Cited by in corpus (27)

• Wild Quiver Gauge Theories
• Instanton moduli spaces and bases in coset conformal field theory
• Ramond sector of super Liouville theory from instantons on an ALE space
• W_3 irregular states and isolated N=2 superconformal field theories
• Parafermionic Liouville field theory and instantons on ALE spaces
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Scheme dependence of instanton counting in ALE spaces
• The universal Racah-Wigner symbol for Uq(osp(1|2))
• A brief review of the 2d/4d correspondences
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• N=2 quiver gauge theories on A-type ALE spaces
• Coset conformal field theory and instanton counting on C^2/Z_p
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Liouville's Imaginary Shadow
• Super-Liouville - Double Liouville correspondence
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• Holomorphic Anomaly in Gauge Theory on ALE space
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Orbifold Vortex and Super Liouville Theory
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Non-rational su(2) cosets and Liouville field theory
• AGT basis in SCFT for c=3/2 and Uglov Polynomials