Matrix models for β-ensembles from Nekrasov partition functions

2009/12/31 by Piotr Sułkowski · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Conjecture #Context (archaeology) #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Instanton #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix model #Measure (data warehouse) #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Vandermonde matrix #hep-th

paper · pdf · doi:10.1007/jhep04(2010)063

published as JHEP 1004:063, 2010 · 36 pages, 3 figures, published version

openalex publication_date 2010/04/01 · arxiv created 2010/04/21 · arxiv updated 2010/04/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We relate Nekrasov partition functions, with arbitrary values of ε₁,ε₂ parameters, to matrix models for β-ensembles. We find matrix models encoding the instanton part of Nekrasov partition functions, whose measure, to the leading order in ε₂ expansion, is given by the Vandermonde determinant to the power β=-ε₁/ε₂. An additional, trigonometric deformation of the measure arises in five-dimensional theories. Matrix model potentials, to the leading order in ε₂ expansion, are the same as in the β=1 case considered in 0810.4944 [hep-th]. We point out that potentials for massive hypermultiplets include multi-log, Penner-like terms. Inclusion of Chern-Simons terms in five-dimensional theories leads to multi-matrix models. The role of these matrix models in the context of the AGT conjecture is discussed.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• Generation of matrix models by Ŵ-operators
• Topological expansion of the Bethe ansatz, and quantum algebraic geometry
• The power of Nekrasov functions
• Zamolodchikov asymptotic formula and instanton expansion in 𝒩 = 2 SUSYNf= 2NcQCD
• A Perturbative Window into Non-Perturbative Physics
• Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
• All order asymptotic expansion of large partitions
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Matrix models for2*theories
• Matrix models, topological strings, and supersymmetric gauge theories
• Instanton counting on blowup. II. K-theoretic partition function

Cited by

• TOWARDS A PROOF OF AGT CONJECTURE BY METHODS OF MATRIX MODELS
• One-cut solution of the β ensembles in the Zhukovsky variable
• Analysis of correlation functions in Toda theory and the Alday-Gaiotto-Tachikawa-Wyllard relation forSU(3)quiver
• Загадки β-деформации

Related

• β-deformed matrix models and the 2d/4d correspondence
• Series over fat partitions: matrix models and discrete ensembles
• Universal objects of the infinite beta random matrix theory
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures