Hamiltonian integrability of the webs of integrable theories

TL;DR

This paper establishes the Hamiltonian integrability of certain recently constructed theories by demonstrating involution of conserved charges and formulating equations of motion as zero curvature Lax connections.

Contribution

It provides the Hamiltonian formulation of these theories and proves their integrability through conserved charges in involution and Lax pair representation.

Findings

Conserved charges are in involution.

Equations of motion can be expressed as zero curvature Lax connections.

Theories are canonically equivalent to known models.

Abstract

We present the Hamiltonian formulation of the recently constructed integrable theories of arXiv:2006.12525. These theories turn out to be canonically equivalent to the sum of an asymmetrically gauged CFT and of the most general $\lambda$-deformed model of arXiv:1812.04033. Using the Hamiltonian formalism, we prove that the full set of conserved charges of the models of arXiv:2006.12525 are in involution, ensuring their Hamiltonian integrability. Finally, we show that the equations of motion of these theories can be put in the form of zero curvature Lax connections.