Large N_c confinement and turbulence

Abstract

We suggest that the transition that occurs at large $N_c$ in the eigenvalue distribution of a Wilson loop may have a turbulent origin. We arrived at this conclusion by studying the complex-valued inviscid Burgers-Hopf equation that corresponds to the Makeenko-Migdal loop equation, and we demonstrate the appearance of a shock in the spectral flow of the Wilson loop eigenvalues. This picture supplements that of the Durhuus-Olesen transition with a particular realization of disorder. The critical behavior at the formation of the shock allows us to infer exponents that have been measured recently in lattice simulations by Narayanan and Neuberger in $d=2$ and $d=3$. Our analysis leads us to speculate that the universal behavior observed in these lattice simulations might be a generic feature of confinement, also in $d=4$ Yang-Mills theory.

4 pages, no figures- Some rewriting - Typos corrected - References completed and some corrected

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• Dysonian dynamics of the Ginibre ensemble
• Introductory lectures to large-N QCD phenomenology and lattice results
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• Products of Independent Quaternion Ginibre Matrices and their Correlation Functions
• Products of Independent Gaussian Random Matrices
• Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics
• Universal shocks in random matrix theory
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• Burgers' equation in 2D SU(N) YM
• Non-analyticity in scale in the planar limit of QCD
• Possible large-N transitions for complex Wilson loop matrices
• Complex Burgers' equation in 2D SU(N) YM
• Universal shocks in the Wishart random matrix ensemble - 1
• Eigenvalue density of Wilson loops in 2D SU(N) YM
• Hydrodynamical spectral evolution for random matrices
• Hydrodynamic Limit of Multiple SLE
• Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD
• Emergent Phase Space Description of Unitary Matrix Model
• Summing free unitary random matrices
• Indications of a non-trivial vacuum in the effective theory of perfect fluids
• Diffusion method in Random Matrix Theory
• Understanding thermalization in a non-Abelian gauge theory in terms of its soft modes
• Exact spectral densities of complex noise-plus-structure random matrices
• Eikonal formulation of large dynamical random matrix models
• Dip-ramp-plateau for Dyson Brownian motion from the identity on $U(N)$
• Two dimensional fermions in four dimensional YM
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• The need for a nonlocal expansion in general relativity
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• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases