Giant Magnons

Abstract

Studies of $\mathcal{N}=4$ super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain. These spin chains have fundamental ``magnon'' excitations which obey a dispersion relation that is periodic in the momentum of the magnons. This result for the dispersion relation was also shown to hold at arbitrary 't Hooft coupling. Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description. The crucial idea is that the momentum is interpreted in the string theory side as a certain geometrical angle. We use these results to compute the energy of a spinning string. We also show that the symmetries that determine the dispersion relation and that constrain the S-matrix are the same in the gauge theory and the string theory. We compute the overall S-matrix at large 't Hooft coupling using the string description and we find that it agrees with an earlier conjecture. We also find an infinite number of two magnon bound states at strong coupling, while at weak coupling this number is finite.

34 pages, 9 figures, latex v2: references added

References in corpus (8)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Quantum corrections to the string Bethe ansatz
• On AdS_5 x S^5 String S-matrix
• On the Singularities of the Magnon S-matrix
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• A Universality Test of the Quantum String Bethe Ansatz
• Dynamics of Flux Tubes in Large N Gauge Theories
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Cited by in corpus (115)

• Finite-size Effects from Giant Magnons
• On String S-matrix, Bound States and TBA
• The all loop AdS4/CFT3 Bethe ansatz
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Dressing and Wrapping
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• String hypothesis for the AdS_5 x S^5 mirror
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• On the Singularities of the Magnon S-matrix
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Wrapping interactions at strong coupling -- the giant magnon
• Three-dimensional N=6 SCFT's and their membrane dynamics
• 1/2-BPS states in M theory and defects in the dual CFTs
• Infinite spin limit of semiclassical string states
• The S-matrix of String Bound States
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Generating AdS String Solutions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• 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
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Pohlmeyer reduction revisited
• Single spike solutions for strings on S2 and S3
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Multispin Giant Magnons
• Strong coupling limit of Bethe Ansatz equations
• Gauge invariant finite size spectrum of the giant magnon
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• The magnon kinematics of the AdS/CFT correspondence
• Finite-Size Effects for Dyonic Giant Magnons
• World-sheet scattering in AdS_5 x S^5 at two loops
• On reduced models for superstrings on AdS_n x S^n
• Magnons, Classical Strings and beta-Deformations
• Quantum Wrapped Giant Magnon
• Solitons and AdS String Solutions
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Moduli Dynamics of AdS_3 Strings
• Finite size effects for giant magnons on physical strings
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
• Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections
• Asymptotic Bethe Ansatz from String Sigma Model on S^3 x R
• A Yangian Double for the AdS/CFT Classical r-matrix
• Spiky Strings, Giant Magnons and beta-deformations
• Three-Spin Giant Magnons in AdS_5xS^5
• Integrable twists in AdS/CFT
• Aspects of emergent geometry in the AdS/CFT context
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• Dilatation operator and the Super Yang-Mills duals of open strings on AdS Giant Gravitons
• Finite-Size Effects for Multi-Magnon States
• Geometry and topology of bubble solutions from gauge theory
• Interacting finite-size magnons
• Large Winding Sector of AdS/CFT
• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Quantum Scattering of Giant Magnons
• Comments on the Boundary Scattering Phase
• Reflecting Magnon Bound States
• On the Scattering Phase for AdS_5 x S^5 Strings
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Dual Spikes; New Spiky String Solutions
• A New and Elementary CP^n Dyonic Magnon
• On the Scattering of Magnon Boundstates
• Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling
• On the anatomy of multi-spin magnon and single spike string solutions
• Giant magnon bound states from strongly coupled N=4 SYM
• Giant magnons and spiky strings on the conifold
• Semiclassical Quantization of the Giant Magnon
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• Dressing the Giant Gluon
• Giant Magnons on CP^3 by Dressing Method
• Dressed Giant Magnons on CP^3
• Magnon-Like Dispersion Relation from M-Theory
• Universal blocks of the AdS/CFT Scattering Matrix
• Strings on conifolds from strong coupling dynamics, part I
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Aspects of Integrability in AdS/CFT Duality
• On the multi-spin magnon and spike solutions from membranes
• A large spin limit of strings on AdS_5 x S^5 in a non-compact sector
• A Topologically Massive Gauge Theory with 32 Supercharges
• Structure of the string R-matrix
• Kinky Strings in AdS_5 x S^5
• Nesting and Dressing
• Giant Magnons under NS-NS and Melvin Fields
• Electrified BPS Giants: BPS configurations on Giant Gravitons with Static Electric Field
• Giant Magnons and Spiky Strings on S^3 with B-field
• Exact solutions for N-magnon scattering
• 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
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• D1-brane in beta-Deformed Background
• Fundamental String and D1-brane in I-brane Background
• A Spin Chain from String Theory
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• A review of integrable deformations in AdS/CFT
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• Zero Modes for the Boundary Giant Magnons
• A strong coupling expansion for N=4 SYM theory and other SCFT's
• The AdS_5 x S^5 superstrings in the generalized light-cone gauge
• N-body Dynamics of Giant Magnons in RxS2
• Semiclassical strings in AdS(3) X S^2
• Spin chain from marginally deformed AdS_3 x S^3
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Strongly coupled large N spectrum of two matrices coupled via a Yang-Mills interaction
• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
• Gauge-String Dualities and Some Applications
• Note About String with Euclidean World-Sheet in AdS(5)xS(5)
• Nambu-Goto Like Action for the AdS_5 x S^5 Superstrings in the Generalized Light-Cone Gauge