Large-Nc confinement and turbulence.

Area of Science:

• Theoretical physics
• Quantum chromodynamics
• Non-perturbative methods

Background:

• The large N_{c} limit in quantum chromodynamics (QCD) simplifies complex interactions.
• Wilson loops are crucial observables for studying confinement in QCD.
• Existing models like the Durhuus-Olesen transition describe aspects of eigenvalue distributions.

Purpose of the Study:

• To investigate the potential turbulent origin of the transition in Wilson loop eigenvalue distributions at large N_{c}.
• To connect theoretical findings with experimental lattice simulation results.
• To explore the universality of confinement phenomena.

Main Methods:

• Studying the complex-valued inviscid Burgers-Hopf equation, which models the Makeenko-Migdal loop equation.
• Analyzing the spectral flow of Wilson loop eigenvalues to identify shock formation.
• Comparing derived critical exponents with recent lattice simulation data.

Main Results:

• Demonstrated the appearance of a shock in the spectral flow of Wilson loop eigenvalues.
• The shock formation provides a specific realization of disorder, supplementing existing models.
• Inferred critical exponents at shock formation that match recent lattice measurements in d=2 and d=3.

Conclusions:

• The transition in Wilson loop eigenvalue distributions at large N_{c} may originate from turbulence.
• The observed shock phenomenon and associated exponents suggest a generic feature of confinement.
• This turbulent picture offers a new perspective on universal behaviors in QCD, potentially extending to d=4 Yang-Mills theory.