Seiberg-Witten theory and matrix models

Abstract

We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves are the Seiberg-Witten curves of the corresponding theories. In consequence of the geometric engineering, the 5-dimensional case provides a novel matrix model formulation of the topological string theory on a wide class of non-compact toric Calabi-Yau manifolds. This approach also unifies and generalizes other matrix models, such as the Eguchi-Yang matrix model, matrix models for bundles over $P^1$, and Chern-Simons matrix models for lens spaces, which arise as various limits of our general result.

43 pages, 5 figures; typos corrected, references added, derivation of the curve in section 4.2 corrected; published version

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Cited by in corpus (37)

• Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Generation of Matrix Models by W-operators
• Ding-Iohara-Miki symmetry of network matrix models
• Penner Type Matrix Model and Seiberg-Witten Theory
• BGWM as Second Constituent of Complex Matrix Model
• A-polynomial, B-model, and Quantization
• Matrix models from operators and topological strings
• Matrix models for $\beta$-ensembles from Nekrasov partition functions
• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• Unitary Integrals and Related Matrix Models
• Exact quantization conditions for the relativistic Toda lattice
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Direct Integration and Non-Perturbative Effects in Matrix Models
• 3d-3d Correspondence Revisited
• Exploring 5d BPS Spectra with Exponential Networks
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Matrix models for 2* theories
• Matrix model from N = 2 orbifold partition function
• Wall Crossing As Seen By Matrix Models
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Quantum curves and conformal field theory
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Refined matrix models from BPS counting
• Confinement and Mayer cluster expansions
• Challenges of beta-deformation
• Beta-ensembles for toric orbifold partition function
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• A matrix model for the topological string II: The spectral curve and mirror geometry
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• Matrix models and stochastic growth in Donaldson-Thomas theory
• BPS states, crystals and matrices
• Aspects géométriques et intégrables des modèles de matrices aléatoires