Large N techniques for Nekrasov partition functions and AGT conjecture

Abstract

The AGT conjecture relates \mathcal{N}=2 4d SUSY gauge theories to 2d CFTs. Matrix model techniques can be used to investigate both sides of this relation. The large N limit refers here to the size of Young tableaux in the expression of the gauge theory partition function. It corresponds to the vanishing of Omega-background equivariant deformation parameters, and should not be confused with the t'Hooft expansion at large number of colors. In this paper, a saddle point approach is employed to study the Nekrasov-Shatashvili limit of the gauge theory, leading to define beta-deformed, or quantized, Seiberg-Witten curve and differential form. Then this formalism is compared to the large N limit of the Dijkgraaf-Vafa beta-ensemble. A transformation law relating the wave functions appearing at both sides of the conjecture is proposed. It implies a transformation of the Seiberg-Witten 1-form in agreement with the definition specified earlier. As a side result, a remarkable property of \mathcal{N}=2 theories emerged: the instanton contribution to the partition function can be determined from the perturbative term analysis.

31 pages, v4 arxiv numbers added to the bibliography

References in corpus (19)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Deforming SW curve
• A direct proof of AGT conjecture at beta = 1
• The Power of Nekrasov Functions
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Seiberg-Witten theory and matrix models
• Spectral Duality Between Heisenberg Chain and Gaudin Model
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
• Deformed Seiberg-Witten Curves for ADE Quivers
• Generalized matrix models and AGT correspondence at all genera
• Seiberg-Witten curve via generalized matrix model
• Virasoro constraint for Nekrasov instanton partition function
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Seiberg-Witten equations and non-commutative spectral curves in Liouville theory

Cited by in corpus (17)

• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• A slow review of the AGT correspondence
• Non-Perturbative Quantum Geometry II
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Quantum geometry from the toroidal block
• Confinement and Mayer cluster expansions
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Notes on Mayer Expansions and Matrix Models
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Seiberg-Witten period relations in Omega background