Integrable sigma models with Haantjes structure on $H_4$ Lie group

Abstract

By solving algebraic relations for the conditions of Haantjes structure on a Lie algebra ${\G}$ and by using the corresponding automorphism group we proceed to classify all inequivalent algebraic Haantjes structures on ${\G}$. In this manner, we obtain 34 inequivalent algebraic Haantjes structures on the $h_4$ Lie algebra. We deform the chiral sigma model on a Lie group by using Haantjes structure on it. Then we try to obtain conditions on this structure such that the deformed sigma model remains to be integrable. Finally, using the $h_4$ Haantjes structures and solving this conditions three new integrable sigma models on the $H_4$ Lie group are obtained.

18 pages

References in corpus (27)

• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• A WZW model based on a non-semi-simple group
• Dual Non-Abelian Duality and the Drinfeld Double
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Jordanian deformations of the AdS_5xS^5 superstring
• Poisson-Lie T-duality
• Integrability of the bi-Yang-Baxter sigma-model
• Yang-Baxter sigma models based on the CYBE
• Integrable double deformation of the principal chiral model
• A Jordanian deformation of AdS space in type IIB supergravity
• A new family of $SU(2)$ symmetric integrable sigma models
• On the geometry of classically integrable two-dimensional non-linear sigma models
• Integrable Generalized Principal Chiral Models
• Yang-Baxter invariance of the Nappi-Witten model
• Haantjes Algebras and Diagonalization
• Haantjes Algebras of Classical Integrable Systems
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• Integrable sigma models with complex and generalized complex structures
• Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Yang-Baxter deformations of the OSP(1|2) WZW model