On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection

Vincent Caudrelier, Matteo Stoppato, Benoit Vicedo

We derive the $2$d Zakharov-Mikhailov action from $4$d Chern-Simons theory. This $2$d action is known to produce as equations of motion the flatness condition of a large class of L…