The SO(N) principal chiral field on a half-line

We investigate the integrability of the SO(N) principal chiral model on a halfline, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in involution. We use an anomaly-counting method to show that at least one non-trivial example survives quantization, compare our results with the proposed reflection matrices, and, based on these, make some preliminary remarks about expected boundary bound-states. 1 The principal chiral field We first recall some preliminaries. A full treatment of the model on the infinite line can be found elsewhere. The principal chiral model may be defined by the lagrangian L = Tr (