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arXiv · 0712.4144

Reflecting Magnon Bound States

Changrim Ahn·Dongsu Bak·Soo-Jong Rey
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Abstract

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.

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Changrim Ahn, Dongsu Bak, Soo-Jong Rey. 2008-02-16. Reflecting Magnon Bound States. https://doi.org/10.1088/1126-6708%2F2008%2F04%2F050

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