Classical Integrability of Chiral QCD2 and Classical Curves

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. Finally, we conclude by showing how 't Hooft's large-N solution is obtained from one of our solutions.