Finite-size Effects from Giant Magnons

Abstract

In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS_5 x S^5, we construct one-soliton solutions carrying finite angular momentum J. In the infinite J limit the solutions reduce to the recently constructed one-magnon configuration of Hofman and Maldacena. The solutions do not satisfy the level-matching condition and hence exhibit a dependence on the gauge choice, which however disappears as the size J is taken to infinity. Interestingly, the solutions do not conserve all the global charges of the psu(2,2|4) algebra of the sigma model, implying that the symmetry algebra of the gauge-fixed string sigma model is different from psu(2,2|4) for finite J, once one gives up the level-matching condition. The magnon dispersion relation exhibits exponential corrections with respect to the infinite J solution. We also find a generalisation of our one-magnon configuration to a solution carrying two charges on the sphere. We comment on the possible implications of our findings for the existence of the Bethe ansatz describing the spectrum of strings carrying finite charges.

42 pages, many figures, movies are available at http://www.aei.mpg.de/~peekas/magnons/ ; v2: Additional comments included and references added

References in corpus (67)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• A semi-classical limit of the gauge/string correspondence
• Type IIB superstring action in AdS_5 x S^5 background
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Bethe Ansatz for Quantum Strings
• Classical/quantum integrability in AdS/CFT
• Giant Magnons
• Multi-spin string solutions in AdS_5 x S^5
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• The su(2|3) Dynamic Spin Chain
• Spinning strings in AdS_5 x S^5 and integrable systems
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Spinning strings in AdS_5 x S^5: new integrable system relations
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors
• Quantum corrections to the string Bethe ansatz
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Matching Higher Conserved Charges for Strings and Spins
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Quantizing three-spin string solution in AdS_5 x S^5
• On AdS_5 x S^5 String S-matrix
• Light-cone Superstring in AdS Space-time
• Spiky strings and single trace operators in gauge theories
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Holography Beyond the Penrose Limit
• Planar N=4 Gauge Theory and the Hubbard Model
• Classical/quantum integrability in non-compact sector of AdS/CFT
• Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• The Algebraic Curve of 1-loop Planar N=4 SYM
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• A Universality Test of the Quantum String Bethe Ansatz
• Stringy sums and corrections to the quantum string Bethe ansatz
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• Semiclassical Bethe Ansatz and AdS/CFT
• Exact expressions for quantum corrections to spinning strings
• New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5
• Bethe Ansatz in Stringy Sigma Models
• The Algebra of Transition Matrices for the AdS_5 x S^5 Superstring
• Two-loop commuting charges and the string/gauge duality
• Strings as Multi-Particle States of Quantum Sigma-Models
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• An action variable of the sine-Gordon model
• Spin chain sigma models with fermions
• The algebra of flat currents for the string on AdS_5 x S^5 in the light-cone gauge
• Asymptotic Bethe Ansatz from String Sigma Model on S^3 x R
• Splitting spinning strings in AdS/CFT
• A nonlocal Poisson bracket of the sine-Gordon model
• Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
• Integrable Heisenberg-van Vleck chains with variable range exchange
• Wound and Rotating Strings in AdS_5 x S^5
• On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
• Splitting strings and chains
• The SU(2) Long Range Bethe Ansatz and Continuous Integrable Systems

Cited by in corpus (182)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• 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
• Four loop twist two, BFKL, wrapping and strings
• Wrapping at four loops in N=4 SYM
• Worldsheet Scattering in AdS_5 x S^5
• Wrapping interactions at strong coupling -- the giant magnon
• Strings on NS-NS Backgrounds as Integrable Deformations
• N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
• On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• Anomalous dimension with wrapping at four loops in N=4 SYM
• Infinite spin limit of semiclassical string states
• The S-matrix of String Bound States
• All-loop Bethe ansatz equations for AdS3/CFT2
• Superdiffusion from emergent classical solitons in quantum spin chains
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• On $T\bar{T}$ deformations and supersymmetry
• Complete 1-loop test of AdS/CFT
• Towards integrability for AdS3/CFT2
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Single spike solutions for strings on S2 and S3
• Multispin Giant Magnons
• Worldsheet spectrum in AdS(4)/CFT(3) correspondence
• Strong coupling limit of Bethe Ansatz equations
• Gauge invariant finite size spectrum of the giant magnon
• A Perspective on Classical Strings from Complex Sine-Gordon Solitons
• Finite size Giant Magnons in the string dual of N=6 superconformal Chern-Simons theory
• S-matrix for magnons in the D1-D5 system
• How Accurate is the Quantum String Bethe Ansatz?
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Exploring the mirror TBA
• Dressing the Giant Magnon II
• Finite-Size Effects for Dyonic Giant Magnons
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• HHL correlators, orbit averaging and form factors
• Quantum Wrapped Giant Magnon
• Two-dimensional S-matrices from unitarity cuts
• Magnons, Classical Strings and beta-Deformations
• Double Wick rotating Green-Schwarz strings
• The Bound State S-Matrix for AdS5 x S5 Superstring
• The one-loop worldsheet S-matrix for the AdS(n) x S(n) x T(10-2n) superstring
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• Finite size effects for giant magnons on physical strings
• $T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry
• Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Giant magnons in TsT-transformed AdS_5 x S^5
• $T\overline{T}$, $\tilde{J}J$, $JT$ and $\tilde{J}T$ deformations
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• The scaling function at strong coupling from the quantum string Bethe equations
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• Finite-size effects in the superconformal beta-deformed N=4 SYM
• Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
• Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections
• Finite Size Giant Magnon
• $T\bar{T}$ deformations as TsT transformations
• Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model
• Spiky Strings, Giant Magnons and beta-deformations
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• Finite-size giant magnons on η-deformed AdS_5 x S^5
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Three-point correlators for giant magnons
• Three-point Correlation functions of Giant magnons with finite size
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• A new derivation of Luscher F-term and fluctuations around the giant magnon
• Finite-Size Effects for Multi-Magnon States
• Interacting finite-size magnons
• Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory
• Giant Magnon in NS5-brane Background
• Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM
• Large Winding Sector of AdS/CFT
• Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
• Correlation functions of magnon and spike
• Zero modes for the giant magnon
• An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
• Scattering of single spikes
• Quantum Scattering of Giant Magnons
• Giant Magnon on Deformed AdS(3)xS(3)
• Review of AdS/CFT Integrability, Chapter III.5: Luscher corrections
• Finite-size effects of Membranes on AdS_4 x S_7
• String solutions in AdS_3 x S^3 x T^4 with NS-NS B-field
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
• On the anatomy of multi-spin magnon and single spike string solutions
• Light-cone gauge Hamiltonian for AdS_4 x CP^3 superstring
• Spiky strings on AdS3 x S3 with NS-NS flux
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• Giant magnons and spiky strings on the conifold
• TTbar deformation and the light-cone gauge
• Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
• Correlation function of dyonic strings
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• Finite-size Effect of the Dyonic Giant Magnons in N=6 super Chern-Simons Theory
• The S-matrix algebra of the AdS2 X S2 superstring
• Comments on World-Sheet Form Factors in AdS/CFT
• Giant Magnons and Singular Curves
• Magnon-Like Dispersion Relation from M-Theory
• Three-point Correlation Function of Giant Magnons in the Lunin-Maldacena background
• Wrapping in maximally supersymmetric and marginally deformed N=4 Yang-Mills
• Aspects of Integrability in AdS/CFT Duality
• More three-point correlators of giant magnons with finite size
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Finite-Size Dyonic Giant Magnons in TsT-transformed $Ad{S}_5\times S^5$
• Finite size effect on the magnon's correlation functions
• On the multi-spin magnon and spike solutions from membranes
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• An improved AFS phase for AdS3 string integrability
• Structure of the string R-matrix
• Toy models for wrapping effects
• Integrable strings for AdS/CFT
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• $T\overline{T}$ Deformations of nonrelativistic models
• Bethe Ansatz solutions for highest states in $\mathcal{N}=4$ SYM and AdS/CFT duality
• Current Algebra and Integrability of Principal Chiral Model on the World-sheet with General Metric
• Factorized Tree-level Scattering in AdS_4 x CP^3
• Structure constants of operators on the Wilson loop from integrability
• Spiky Strings on NS5-branes
• Integrable Subsectors from Holography
• Giant Magnons and Spiky Strings on S^3 with B-field
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• Near Flat Space limit of strings on AdS_4 x CP^3
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
• A note on two-spin magnon-like energy-charge relations from M-theory viewpoint
• Multispin magnons on deformed $Ad{S}_3\times S^3$
• D1-brane in beta-Deformed Background
• Spiky Strings in AdS(4) X CP**3 with Neveu-Schwarz Flux
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• Finite-size effect of η-deformed AdS_5 x S^5 at strong coupling
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• The Near-Flat-Space and BMN Limits for Strings in AdS4 x CP3 at One Loop
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Zero Modes for the Boundary Giant Magnons
• SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling
• Light-Cone Gauge in Non-Relativistic AdS${}_5\times$S${}^5$ String Theory
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Large-Spin Expansions of GKP Strings
• Reduced Sigma-Model on O(N): Hamiltonian Analysis and Poisson Bracket of Lax Connection
• Giant magnon-like solution in Sch_5 x S^5
• Rotating Strings in AdS(4) X CP(3) with B-NS holonomy
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes
• The AdS_5 x S^5 superstrings in the generalized light-cone gauge
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Close to the Giant Magnons
• Correlation functions of the ABJM model
• Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
• Spiky strings in de Sitter space
• Some three-point correlation functions in the eta-deformed AdS_5 x S^5
• Real and Virtual Bound States in Lüscher Corrections for CP3 Magnons
• Leading finite-size effects on some three-point correlators in AdS_5 x S^5
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Giant magnons and non-maximal giant gravitons
• Note About Integrability of Non-Relativistic String
• The plane-wave limit of ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• Wrapping effects in supersymmetric gauge theories
• Boundary Giant Magnons and Giant Gravitons
• Giant Spinons
• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
• Leading finite-size effects on some three-point correlators in TsT-deformed AdS_5 x S^5
• On Rotating and Oscillating Four-Spin Strings in AdS5 X S5
• The Omega-Infinity Limit of Single Spikes
• Semiclassical quantization of the mixed-flux AdS${}_3$ giant magnon
• Finite Size Effect from Classical Strings in deformed AdS${}_3\times$ S${}^3$
• On finite size corrections to the dispersion relations of giant magnon and single spike on γ-deformed T^{1,1}
• Finite size effect from classical strings in $Ad{S}_3\times S^3$ with NS-NS flux
• Canonical Analysis of New Non-Relativistic String Action and Uniform Light-Cone Gauge Formulation
• Unitarity methods for scattering in two dimensions
• New Non-Relativistic String in AdS(5)xS(5)
• Large-Spin Expansions of Giant Magnons
• P-Branes Dynamics, AdS/CFT and Correlation Functions
• Some semiclassical structure constants for AdS_4 x CP^3
• Perturbations of giant magnons and single spikes in $\mathbb{R}\times S^2$
• On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes