Classically integrable boundary conditions for symmetric-space sigma models release_wu7nccsiynei5fvh7jp7xdquvu

Abstract

We investigate boundary conditions for the nonlinear sigma model on the compact symmetric space G/H, where H ⊂ 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 × G/G, they reproduce known results for the principal chiral model.
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