Burgers' equation in 2D SU(N) YM

Abstract

It is shown that the logarithmic derivative of the characteristic polynomial of a Wilson loop in two dimensional pure Yang Mills theory with gauge group SU(N) exactly satisfies Burgers' equation, with viscosity given by 1/(2N). The Wilson loop does not intersect itself and Euclidean space-time is assumed flat and infinite. This result provides a precise framework in 2D YM for recent observations of Blaizot and Nowak and was inspired by their work.

Final version -- accepted for publication in PLB - fixed abstract listing

References in corpus (8)

• Infinite N phase transitions in continuum Wilson loop operators
• Large N_c confinement and turbulence
• Universality of large N phase transitions in Wilson loop operators in two and three dimensions
• Multiplying unitary random matrices - universality and spectral properties
• Diffusion of Wilson Loops
• A large N phase transition in the continuum two dimensional SU(N) X SU(N) principal chiral model
• Tunneling in two dimensional QCD
• A Linear Equation for Wilson Loops

Cited by in corpus (18)

• SU(N) gauge theories at large N
• Introductory lectures to large-N QCD phenomenology and lattice results
• Universal shocks in random matrix theory
• Non-analyticity in scale in the planar limit of QCD
• 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
• Emergent Phase Space Description of Unitary Matrix Model
• Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD
• Integrable models from PT-symmetric deformations
• Eikonal formulation of large dynamical random matrix models
• Two dimensional fermions in four dimensional YM
• Confinement, Turbulence and Diffraction Catastrophes
• Hydrodynamics of the Polyakov Line in SU$(N_c)$ Yang-Mills
• Functional Equations Solving Initial-Value Problems of Complex Burgers-Type Equations for One-Dimensional Log-Gases
• Remarks on correlators of Polyakov Loops
• Scale invariant behavior in a large N matrix model
• Eigenvalue density of Wilson loops in 2D SU(N) YM at large N