Classical integrability of chiral $QCD_{2}$ and classical curves

TL;DR

This paper demonstrates the classical integrability of chiral QCD2 in lightcone gauge by showing its equations of motion have a Lax form, revealing infinite conserved quantities, and relates solutions to classical curves, especially for SU(2).

Contribution

It establishes the classical integrability of chiral QCD2 and explicitly connects solutions to classical curves for the SU(2) gauge group.

Findings

Equations of motion have Lax form indicating integrability.

Solutions correspond to a large class of classical curves.

Explicit solutions and associated fermionic fields are constructed.

Abstract

In this letter, classical chiral $QCD_{2}$ is studied in the lightcone gauge $A_{-}=0$. The once integrated equation of motion for the current is shown to be of the Lax form, which demonstrates an infinite number of conserved quantities. Specializing to gauge group SU(2), we show that solutions to the classical equations of motion can be identified with a very large class of curves. We demonstrate this correspondence explicitly for two solutions. The classical fermionic fields associated with these currents are then obtained.