Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the ‘tensor product graph’ for solutions of the Yang-Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions. 1 The principal chiral model with boundary 1.1 Classical boundary conditions and conserved charges In a recent paper [1] (to which the reader is referred for more detail and references), two of us explored the classical integrability of the principal chiral model (PCM) with boundary, and the corresponding quantum boundary S-matrices. The model is defined by the action L = 1 2 Tr ( ∂μg ∂g ) , (1.1) where the field g(x) takes values in a compact Lie group G, and is defined in 1+1D Minkowski spacetime with −∞ < x ≤ 0. emails: gwd2, nm15, bjs108 @york.ac.uk