β-deformed matrix model and Nekrasov partition function

Abstract

We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional \mathcal{N}=2, SU(2) supersymmetric gauge theories with N_F=2,3 and 4. By evaluating the resolvent using the loop equation for general β, we explicitly construct the first half-genus correction to the free energy and demonstrate the result coincides with the corresponding Nekrasov partition function with general Ω-background, including higher instanton contributions after modifying the relation of the Coulomb branch parameter with the filling fraction. Our approach complements the proof using the Selberg integrals directly which is useful to find the contribution in the series of instanton numbers for a given deformation parameter.

25 pages

References in corpus (16)

• 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)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Asymptotically free N=2 theories and irregular conformal blocks
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Seiberg-Witten theory, matrix model and AGT relation
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Selberg Integral and SU(N) AGT Conjecture
• Generalized matrix models and AGT correspondence at all genera
• Seiberg-Witten curve via generalized matrix model
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• An(1) Affine Quiver Matrix Model

Cited by in corpus (15)

• Matrix models for irregular conformal blocks and Argyres-Douglas theories
• 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
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Confinement and Mayer cluster expansions
• Argyres-Douglas theories and Liouville Irregular States
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Irregular conformal block, spectral curve and flow equations
• Parametric dependence of irregular conformal block
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Notes on Mayer Expansions and Matrix Models
• Multicritical points of unitary matrix model with logarithmic potential identified with Argyres-Douglas points
• Irregular conformal block and its matrix model
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f=2n-2$ flavors