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.

32 pages, minor changes, version accepted in Nucl. Phys. B

References in corpus (12)

• An Integrable Deformation of the AdS5 x S5 Superstring
• The all-loop non-Abelian Thirring model and its RG flow
• Integrable flows between exact CFTs
• Assembling integrable sigma-models as affine Gaudin models
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
• RG flows of integrable $\sigma$-models and the twist function
• Strong integrability of $\lambda$-deformed models
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Field theory and $\lambda$-deformations: Expanding around the identity
• Webs of integrable theories
• $\lambda$-deformations in the upper-half plane

Cited by in corpus (4)

• 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