Classically integrable boundary conditions for symmetric-space sigma models

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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 $\sigma$ 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 $\sigma$. 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
Original languageEnglish
Pages (from-to)221-227
JournalPhysical Letters B
Volume588
Issue number3-4
DOIs
Publication statusPublished - May 2004

Keywords

  • hep-th

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