Reflecting Magnon Bound States

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.

cover+15 pages, 2 figures; v2. minor changes, references added; v3. further minor changes

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Cited by in corpus (23)

• Integrable Wilson loops
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• Holographic Correlation Functions for Open Strings and Branes
• Near Horizon Limits of Massless BTZ and Their CFT Duals
• Reflecting magnons from D7 and D5 branes
• Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory
• Correlation functions of magnon and spike
• The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons
• The Bethe Ansatz Equations for Reflecting Magnons
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Open Perturbatively Long-Range Integrable gl(N) Spin Chains
• Yangian symmetry of boundary scattering in AdS/CFT and the explicit form of bound state reflection matrices
• Bethe ansatz equations for open spin chains from giant gravitons
• Issues on magnon reflection
• On the reflection of magnon bound states
• Zero Modes for the Boundary Giant Magnons
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• Reflection algebra, Yangian symmetry and bound-states in AdS/CFT
• Defects and Dressed Boundaries in Complex Sine-Gordon Theory
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices