Classically integrable boundary conditions for symmetric-space sigma models

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.

8 pages. v2 has an introduction added and a few minor corrections

References in corpus (5)

• Boundary remnant of Yangian symmetry and the structure of rational reflection matrices
• Rational K-matrices and representations of twisted Yangians
• Boundary scattering, symmetric spaces and the principal chiral model on the half-line
• Integrable Boundary Conditions and Reflection Matrices for the O(N) Nonlinear Sigma Model
• Classical O(N) nonlinear sigma model on the half line: a study on consistent Hamiltonian description

Cited by in corpus (11)

• Introduction to Yangian symmetry in integrable field theory
• Lectures on Yangian Symmetry
• Classical Open String Integrability
• Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)xSO(n) and Sp(2n)/Sp(n)xSp(n)
• Achiral boundaries and the twisted Yangian of the D5-brane
• D-branes in $\lambda$-deformations
• On integrable boundaries in the 2 dimensional $O(N)$ $\sigma$-models
• Integrable crosscaps in classical sigma models
• Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
• Giant magnons and non-maximal giant gravitons
• Superfield Lax formalism of supersymmetric sigma model on symmetric spaces