Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories

Abstract

The conjecture about the correspondence between instanton partition functions in the N=2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the case of the N=1 supersymmetric conformal blocks. We find that the necessary modification of the moduli space of instantons requires additional restriction of Z(2)-symmetry. This leads to an explicit form of the N=1 superconformal blocks in terms of Young diagrams with two sorts of cells.

18 pages, misprints corrected, formula 5.8 is improved, references added

References in corpus (8)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
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• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
• N=1 SUSY Conformal Block Recursive Relations
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Cited by in corpus (76)

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• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• Q-deformed Painleve tau function and q-deformed conformal blocks
• The Liouville side of the Vortex
• W_3 irregular states and isolated N=2 superconformal field theories
• A slow review of the AGT correspondence
• Whittaker pairs for the Virasoro algebra and the Gaiotto - BMT states
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
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• 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
• Exact results for $\mathcal{N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• Toda Theory From Six Dimensions
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• Conformal blocks of W_N Minimal Models and AGT correspondence
• Superconformal field theory and Jack superpolynomials
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• Compactification on the Ω-background and the AGT correspondence
• A brief review of the 2d/4d correspondences
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• 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
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• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• On the six-dimensional origin of the AGT correspondence
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• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations
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• Liouville's Imaginary Shadow
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• q-Vertex Operator from 5D Nekrasov Function
• Super-Liouville - Double Liouville correspondence
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• N=2 superconformal blocks and instanton partition functions
• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• Vortices on Orbifolds
• Conformal blocks of Chiral fields in N=2 SUSY CFT and Affine Laumon Spaces
• Holomorphic Anomaly in Gauge Theory on ALE space
• Double Quiver Gauge Theory and BPS/CFT Correspondence
• Recurrence relations for toric N=1 superconformal blocks
• Comments on fusion matrix in N=1 super Liouville field theory
• Comments on chiral algebras and $\Omega$-deformations
• $\widehat{\mathfrak{sl}}(n{)}_N$ 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
• c-Recursion for multi-point superconformal blocks. NS sector
• Second Order RG Flow in General su(2) Coset Models
• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Virasoro Constraint for Uglov Matrix Model
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• Super-spectral curve of irregular conformal blocks
• The light asymptotic limit of conformal blocks in $\mathcal{N}=1$ super Liouville field theory
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• AGT basis in SCFT for c=3/2 and Uglov Polynomials
• Super-Whittaker vector at c=3/2
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