Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$

Abstract

We consider a particular large-radius limit of the worldsheet $S$-matrix for strings propagating on $Ad{S}_5\times S^5$. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the full theory, and may be easier to solve directly. The $S$ matrix of the limiting theory is non-trivial, and receives contributions to all orders in the ${\alpha }^{\prime }$ expansion. We analyze a guess for the full worldsheet $S$ matrix that was formulated recently by Beisert, Hernandez and Lopez, and Beisert, Eden, and Staudacher, and take the corresponding limit. After doing a Borel resummation we find that the proposed $S$ matrix reproduces the expected results in the giant-magnon region. In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the $S$ matrix.

39 pages 5 figures; v2: Statement about singularities at $u_1-u_2=i$ corrected; v3: Typos, signs and coefficients corrected

References in corpus (12)

• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Quantum corrections to the string Bethe ansatz
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Magnon Bound States and the AdS/CFT Correspondence
• Dyonic Giant Magnons
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• On the Hopf algebra structure of the AdS/CFT S-matrix
• Spiky strings and giant magnons on S5
• Dressing the Giant Magnon
• Integrability and non-perturbative effects in the AdS/CFT correspondence

Cited by in corpus (48)

• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• On String S-matrix, Bound States and TBA
• On the Singularities of the Magnon S-matrix
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• Complete 1-loop test of AdS/CFT
• Towards integrability for AdS3/CFT2
• Single spike solutions for strings on S2 and S3
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Gauge invariant finite size spectrum of the giant magnon
• Strong coupling limit of Bethe Ansatz equations
• S-matrix for magnons in the D1-D5 system
• Finite-Size Effects for Dyonic Giant Magnons
• World-sheet scattering in AdS_5 x S^5 at two loops
• Konishi operator at intermediate coupling
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
• Yangians, S-matrices and AdS/CFT
• A Yangian Double for the AdS/CFT Classical r-matrix
• Spiky Strings, Giant Magnons and beta-deformations
• New Dressing Factors for AdS3/CFT2
• One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• Interacting finite-size magnons
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Quantum Scattering of Giant Magnons
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• On the anatomy of multi-spin magnon and single spike string solutions
• Giant magnons and spiky strings on the conifold
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• Giant Magnons on CP^3 by Dressing Method
• Aspects of Integrability in AdS/CFT Duality
• On the multi-spin magnon and spike solutions from membranes
• Structure of the string R-matrix
• Factorized Tree-level Scattering in AdS_4 x CP^3
• Giant Magnons and Spiky Strings on S^3 with B-field
• Near-flat space limit and Einstein manifolds
• A note on two-spin magnon-like energy-charge relations from M-theory viewpoint
• Near Flat Space limit of strings on AdS_4 x CP^3
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• Semiclassical strings in AdS(3) X S^2
• The Ising model and planar N=4 Yang-Mills
• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
• Nambu-Goto Like Action for the AdS_5 x S^5 Superstrings in the Generalized Light-Cone Gauge
• Perturbations of giant magnons and single spikes in $\mathbb{R}\times S^2$