Exact solution for mean energy of 2d Dyson gas at beta = 1

Abstract

Mean Coulomb energy of 2d Dyson gas in quadratic potential is examined from combinatorial viewpoint. For beta = 1, we find a recursive relation on mean energy and obtain its exact (finite N) solution in closed form in terms of the hypergeometric function 3F2. Using this exact solution, we derive the large-N asymptotic expansion of mean energy and show, that this expansion contains half-integer powers of N.

10 pages, 1 figure

References in corpus (23)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On non-conformal limit of the AGT relations
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Recursion relations in CFT and N=2 SYM theory
• On AGT conjecture
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Recursive representation of the torus 1-point conformal block
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Large N expansion for the 2D Dyson gas
• A direct proof of AGT conjecture at beta = 1
• The Power of Nekrasov Functions
• On Combinatorial Expansions of Conformal Blocks
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Proving AGT relations in the large-c limit
• On AGT Conjecture for Pure Super Yang-Mills and W-algebra
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
• Check of AGT Relation for Conformal Blocks on Sphere
• On AGT description of N=2 SCFT with N_f=4

Cited by in corpus (17)

• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Matrix Models for Random Partitions
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Exact and asymptotic features of the edge density profile for the one component plasma in two dimensions
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials
• Challenges of beta-deformation
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Exact Energy Computation of the One Component Plasma on a Sphere for Even Values of the Coupling Parameter
• Beta Deformation and Superpolynomials of (n,m) Torus Knots
• Method of computation of energies in the fractional quantum Hall effect regime
• Exact Energy Expansion of the two-dimensional Dyson Gas for Odd Values of $\Gamma /2$