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 (11)

• Giant Magnons
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Physics and Mathematics of Calogero particles
• Quantum corrections to the string Bethe ansatz
• On AdS_5 x S^5 String S-matrix
• Magnon Bound States and the AdS/CFT Correspondence
• Dyonic Giant Magnons
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
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• Strong coupling limit of Bethe Ansatz equations
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• Giant Magnons
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• 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
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• 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
• Towards integrability for AdS3/CFT2
• 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
• The Quantum Deformed Mirror TBA I
• Wronskian Solution for AdS/CFT Y-system
• Konishi operator at intermediate coupling
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Classical r-matrix of the su(2|2) SYM spin-chain
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• A Yangian Double for the AdS/CFT Classical r-matrix
• New Dressing Factors for AdS3/CFT2
• Interacting finite-size magnons
• Large Winding Sector of AdS/CFT
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Quantum Scattering of Giant Magnons
• Comments on the Boundary Scattering Phase
• 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
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• Minimal solution of the AdS/CFT crossing equation
• Giant Magnons on CP^3 by Dressing Method
• Aspects of Integrability in AdS/CFT Duality
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• On the $Ad{S}_5/CF{T}_4$ TBA and its analytic properties
• 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
• The Ising model and planar N=4 Yang-Mills
• On the dressing phase in the SL(2) Bethe Ansatz
• Microscopic formulation of the S-matrix in AdS/CFT
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon
• Exact Results in Supersymmetric Gauge Theories
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• On the singularities of the R-R AdS_3 x S^3 x T^4 S matrix