A Linear Equation for Wilson Loops
نویسنده
چکیده
The Makeenko-Migdal loop equation is non-linear and first order in the area derivative, but we show that for simple loops in QCD2 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.
منابع مشابه
Wilson wavelets for solving nonlinear stochastic integral equations
A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...
متن کاملA New Type of Loop Equations
We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight lightlike Wilson lines. In the case of N = 1 in ten dimensions they close for any light-like Wilson loop. Upon dimensional reduction to N = 4 SYM in four dimensions, these loops become exactly the chiral loops which can be evaluated semiclassically, in the strong ...
متن کاملTopics in Cusped/Lightcone Wilson Loops
I review several old/new approaches to the string/gauge correspondence for the cusped/lightcone Wilson loops. The main attention is payed to SYM perturbation theory calculations at two loops and beyond and to the cusped loop equation. These three introductory lectures were given at the 48 Cracow School of Theoretical Physics: “Aspects of Duality”, June 13-22, 2008, Zakopane, Poland.
متن کاملPartonic Distributions for Large X and Renormalization of Wilson Loop *
We discuss the relation between partonic distributions near the phase space boundary and Wilson loop expectation values calculated along paths partially lying on the light-cone. Due to additional light-cone singularities, multiplicative renormalizability for these expectation values is lost. Nevertheless we establish the renormalization group equation for the light like Wilson loops and show th...
متن کاملStructure function for large x and renormalization of Wilson loop ∗
We discuss the relation between hard distributions near the phase space boundary, such as structure function for large x, and Wilson loop expectation values calculated along paths partially lying on the light-cone. Due to additional light cone singularities, multiplicative renormalizability for these expectation values is lost. Nevertheless we establish the renormalization group equation for th...
متن کامل