Possible large-N transitions for complex Wilson loop matrices

Abstract

It is shown that a very simple multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a non-perturbative regime at a point where the smoothness of some quantities breaks down. A generic complex Wilson loop matrix in a field theory admitting a 't Hooft planar limit could display a phase transition in that limit as nonlinear effects become dominating over linear ones.

45 pages, 4 compound figures

References in corpus (5)

• 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
• Tunneling in two dimensional QCD
• A Linear Equation for Wilson Loops

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• Eigenvalue density of Wilson loops in 2D SU(N) YM
• Summing free unitary random matrices
• Eikonal formulation of large dynamical random matrix models
• PDE methods in random matrix theory
• Two dimensional fermions in four dimensional YM
• The Brown measure of a family of free multiplicative Brownian motions
• Composition of quantum operations and products of random matrices
• Eigenvalue density of Wilson loops in 2D SU(N) YM at large N