Instantons and 2d Superconformal field theory

Abstract

A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which corresponds to the particular case k=m=2. The construction is based on the conjectural relation between moduli spaces of SU(2) instantons on R^4/Z_2 and algebras like \hat{gl}(2)_2\times NSR. This conjecture is confirmed by checking the coincidence of number of fixed points on such instanton moduli space with given instanton number N and dimension of subspace degree N in the representation of such algebra.

13 pages, exposition improved, references added

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Cited by in corpus (49)

• 4d Index to 3d Index and 2d TQFT
• Instanton moduli spaces and bases in coset conformal field theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Integrable structure, W-symmetry and AGT relation
• Webs of W-algebras
• Ramond sector of super Liouville theory from instantons on an ALE space
• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• The Liouville side of the Vortex
• A slow review of the AGT correspondence
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Parafermionic Liouville field theory and instantons on ALE spaces
• Coset conformal blocks and N=2 gauge theories
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• Exact results for $\mathcal{N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• Superconformal field theory and Jack superpolynomials
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Matrix model from N = 2 orbifold partition function
• Scheme dependence of instanton counting in ALE spaces
• A brief review of the 2d/4d correspondences
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• N=2 quiver gauge theories on A-type ALE spaces
• Coset conformal field theory and instanton counting on C^2/Z_p
• Vortex counting from field theory
• AGT/Z${}_2$
• N=1 superconformal blocks with Ramond fields from AGT correspondence
• q-Vertex Operator from 5D Nekrasov Function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Super-Liouville - Double Liouville correspondence
• Beta-ensembles for toric orbifold partition function
• N=2 superconformal blocks and instanton partition functions
• On the Renormalization Group Flow in Two Dimensional Superconformal Models
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• Conformal blocks of Chiral fields in N=2 SUSY CFT and Affine Laumon Spaces
• Recurrence relations for toric N=1 superconformal blocks
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
• Second Order RG Flow in General su(2) Coset Models
• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• The light asymptotic limit of conformal blocks in $\mathcal{N}=1$ super Liouville field theory
• Orbifold Vortex and Super Liouville Theory
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Super-Whittaker vector at c=3/2
• AGT basis in SCFT for c=3/2 and Uglov Polynomials
• Coloured refined topological vertices and parafermion conformal field theories