Hamiltonian integrability of the webs of integrable theories

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.

arXiv comment32 pages, minor changes, version accepted in Nucl. Phys. B

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• Deformed WZW Models and Hodge Theory -- Part I
• The massless S-matrix of integrable $\sigma$-models
• Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production
• Integrable branes in generalized $\lambda$-deformations