Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality

Abstract

Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^{\ast }SU(2)\simeq SU(2)⋉{\mathbb{R}}^3$. The corresponding dual models are obtained through $O(3,3)$ duality transformations and result to be defined on the group $SB(2,\mathbb{C})$, which is the Poisson-Lie dual of $SU(2)$ in the Iwasawa decomposition of the Drinfel'd double $SL(2,\mathbb{C})=SU(2)\bowtie SB(2,\mathbb{C})$.These dual models provide an explicit realization of Poisson-Lie T-duality. A doubled generalized parent action is then built on the tangent space $TSL(2,\mathbb{C})$. Furthermore, a generalization of the $SU(2)$ PCM with a WZ term is shortly discussed.

arXiv comment25 pages, Contribution to the Proceedings of Corfu Summer Institute 2019 "Schools and Workshops on Elementary Particle Physics and Gravity"

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Cited by in corpus (5)

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• Topological and dynamical aspects of Jacobi sigma models
• The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective
• Extended Field Theories as higher Kaluza-Klein theories
• On the classical Integrability of Poisson-Lie T-dual WZW models