On the Singularities of the Magnon S-matrix

Abstract

We investigate the analytic structure of the magnon S-matrix in the spin-chain description of planar $\mathcal{N}=4$ SUSY Yang-Mills/$Ad{S}_5\times S^5$ strings. Semiclassical analysis suggests that the exact S-matrix must have a large family of poles near the real axis in momentum space. In this article we show that these are double poles corresponding to the exchange of pairs of BPS magnons. Their locations in the complex plane are uniquely fixed by the known dispersion relation for the BPS particles. The locations precisely agree with the recent conjecture for the $S$ matrix by Beisert, Hernandez, Lopez, Eden and Staudacher (hep-th/0609044 and hep-th/0610251). These poles do not signal the presence of new bound states. In fact, a certain non-BPS localized classical solution, which was thought to give rise to new bound states, can actually decay into a pair of BPS magnons.

40 pages, 14 figures; typos corrected, references added

References in corpus (2)

• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Strong coupling limit of Bethe Ansatz equations

Cited by in corpus (40)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• On String S-matrix, Bound States and TBA
• The all loop AdS4/CFT3 Bethe ansatz
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Wrapping interactions at strong coupling -- the giant magnon
• The S-matrix of String Bound States
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• Complete 1-loop test of AdS/CFT
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Strong coupling limit of Bethe Ansatz equations
• The Four-Loop Dressing Phase of N=4 SYM
• Finite-Size Effects for Dyonic Giant Magnons
• World-sheet scattering in AdS_5 x S^5 at two loops
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Yangian Double for the AdS/CFT Classical r-matrix
• Interacting finite-size magnons
• Large Winding Sector of AdS/CFT
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Comments on the Boundary Scattering Phase
• Quantum Scattering of Giant Magnons
• Reflecting Magnon Bound States
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• The Bethe Ansatz Equations for Reflecting Magnons
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Minimal solution of the AdS/CFT crossing equation
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• Giant Magnons on CP^3 by Dressing Method
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Aspects of Integrability in AdS/CFT Duality
• Issues on magnon reflection
• Exact solutions for N-magnon scattering
• On the origin of the dressing phase in N=4 Super Yang-Mills
• N-body Dynamics of Giant Magnons in RxS2
• Analytic Bethe Ansatz and Baxter equations for long-range psl(2|2) spin chain
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Microscopic formulation of the S-matrix in AdS/CFT
• On the dressing phase in the SL(2) Bethe Ansatz
• The Ising model and planar N=4 Yang-Mills