Eigenvalue Distributions in Yang-Mills Integrals

Abstract

We investigate one-matrix correlation functions for finite SU(N) Yang-Mills integrals with and without supersymmetry. We propose novel convergence conditions for these correlators which we determine from the one-loop perturbative effective action. These conditions are found to agree with non-perturbative Monte Carlo calculations for various gauge groups and dimensions. Our results yield important insights into the eigenvalue distributions rho(lambda) of these random matrix models. For the bosonic models, we find that the spectral densities rho(lambda) possess moments of all orders as N -> Infinity. In the supersymmetric case, rho(lambda) is a wide distribution with an N-independent asymptotic behavior rho(lambda) ~ lambda^(-3), lambda^(-7), lambda^(-15) for dimensions D=4,6,10, respectively.

8 pages, 6 figures, some corrections

References in corpus (5)

• D-particle bound states and generalized instantons
• Monte Carlo Approach to M-Theory
• Dynamical Aspects of Large N Reduced Models
• Finite Yang-Mills Integrals
• Matrix String Partition Functions

Cited by in corpus (41)

• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Exact lattice supersymmetry
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Convergent Yang-Mills Matrix Theories
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Towards lattice simulation of the gauge theory duals to black holes and hot strings
• The Phase Structure of Low Dimensional Large N Gauge Theories on Tori
• Extracting black hole physics from the lattice
• Multi-matrix models and emergent geometry
• Phases of one dimensional large N gauge theory in a 1/D expansion
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Yang-Mills Integrals for Orthogonal, Symplectic and Exceptional Groups
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• High temperature expansion in supersymmetric matrix quantum mechanics
• First results from simulations of supersymmetric lattices
• Bulk Witten Indices and the Number of Normalizable Ground States in Supersymmetric Quantum Mechanics of Orthogonal, Symplectic and Exceptional Groups
• Phase Structure of Lattice N=4 Super Yang-Mills
• Gaussian and Mean Field Approximations for Reduced Yang-Mills Integrals
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral
• Large N limit of the IKKT matrix model
• Rotational Symmetry Breaking in Multi-Matrix Models
• On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory
• Yang-Mills Matrix Theory
• N=2 3d-Matrix Integral with Myers Term
• Yang-Mills Integrals
• A practical solution to the sign problem in a matrix model for dynamical compactification
• On the supersymmetric formulation of Unitary Matrix Model of type IIB
• Adding a Myers Term to the IIB Matrix Model
• Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature
• A Renormalization Group Approach to A Yang-Mills Two Matrix Model
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II
• Introduction to Monte Carlo for Matrix Models
• Polyakov Lines in Yang-Mills Matrix Models
• Yang-Mills Integrals
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• Partition Functions of Reduced Matrix Models with Classical Gauge Groups
• SL(2,R) matrix model and supersymmetric Yang-Mills integrals
• The dynamics of zero modes in lattice gauge theory -- difference between SU(2) and SU(3) in 4D