A Linear Equation for Wilson Loops

Abstract

The Makeenko-Migdal loop equation is non-linear and first order in the area derivative, but we show that for simple loops in QCD${}_2$ it is possible to reformulate this equation as a linear equation with second order derivatives. This equation is a bound state Schrödinger equation with a three dimensional Coulomb potential. Thus, loop dynamics leads to a surprising new picture of confinement, where this phenomenon is due to a (bound state) localization in loop space, with the Wilson loops decaying exponentially outside a characteristic radius.

6 pages. Some comments added

References in corpus (5)

• Infinite N phase transitions in continuum Wilson loop operators
• Mastering the Master Field
• Gauge fields - strings duality and the loop equation
• Loop dynamics and AdS/CFT correspondence
• Exact beta function from the holographic loop equation of large-N QCD_4

Cited by in corpus (6)

• SU(N) gauge theories at large N
• Introductory lectures to large-N QCD phenomenology and lattice results
• Large N_c confinement and turbulence
• Burgers' equation in 2D SU(N) YM
• Possible large-N transitions for complex Wilson loop matrices
• A large N phase transition in the continuum two dimensional SU(N) X SU(N) principal chiral model