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arXiv · hep-th/0402182

Classically integrable boundary conditions for symmetric-space sigma models

N. J. MacKay·C. A. S. Young
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Abstract

We investigate boundary conditions for the nonlinear sigma model on the compact symmetric space $G/H$, where $H \subset G$ is the subgroup fixed by an involution $σ$ of $G$. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions in correspondence with involutions which commute with $σ$. Applied to $SO(3)/SO(2)$, the nonlinear sigma model on $S^2$, these yield the great circles as boundary submanifolds. Applied to $G \times G/G$, they reproduce known results for the principal chiral model.

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N. J. MacKay, C. A. S. Young. 2004-03-16. Classically integrable boundary conditions for symmetric-space sigma models. https://doi.org/10.1016/j.physletb.2004.03.037

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