Burgers' equation in 2D SU(N) YM

TL;DR

This paper demonstrates that the logarithmic derivative of the Wilson loop's characteristic polynomial in 2D SU(N) Yang-Mills theory exactly obeys Burgers' equation, linking gauge theory to a fundamental nonlinear PDE.

Contribution

It establishes a precise connection between Wilson loops in 2D YM and Burgers' equation, with explicit viscosity related to the gauge group size N.

Findings

The logarithmic derivative satisfies Burgers' equation with viscosity 1/(2N).

The result provides a theoretical framework for recent observations in 2D YM.

The analysis assumes non-intersecting Wilson loops in flat, infinite space-time.

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.