The Bethe ansatz equations for reflecting magnons

We derive the Bethe ansatz equations on the half line for particles interacting through factorized S-matrices invariant relative to the centrally extended su(2|2) Lie superalgebra and su(1|2) open boundaries. These equations may be of relevance for the study of the spectrum of open strings on AdS5×S5 background attached to Y=0 giant graviton branes. A one-dimensional spin chain Hamiltonian associated to this system is also derived.