Reflecting Magnon Bound States

In N = 4 super Yang-Mills spin chain, we compute reflection amplitudes of magnon bound-state off giant graviton. We first compute the reflection amplitude off Y = 0 brane boundary and compare it with the scattering amplitude between two magnon bound-states in the bulk. We find that analytic structure of the two amplitudes are intimately related each other: the boundary reflection amplitude is a square-root of the bulk scattering amplitude. Using such relation as a guide and taking known results at weak and strong coupling limits as inputs, we find the reflection amplitude of an elementary magnon off Z = 0 giant graviton boundary. The reflection phase-factor is shown to solve crossing and unitarity relations. We then compute the reflection amplitude of magnon bound-state off the Z = 0 brane boundary and observe that its analytic structures are again intimately related to the bulk scattering and the Y = 0 boundary reflection amplitudes. We also take dyonic giant magnon limit of these reflection amplitudes and confirm that their phase-shifts agree completely with string worldsheet computations based on complex sine-Gordon soliton scattering.