The complete AdS_3 x S^3 x T^4 worldsheet S-matrix

Abstract

We derive the non-perturbative worldsheet S matrix for fundamental excitations of Type IIB superstring theory on AdS_3 x S^3 x T^4 with Ramond-Ramond flux. To this end, we study the off-shell symmetry algebra of the theory and its representations. We use these to determine the S matrix up to scalar factors and we derive the crossing equations that these scalar factors satisfy. Our treatment automatically includes fundamental massless excitations, removing a long-standing obstacle in using integrability to study the AdS_3/CFT_2 correspondence. The present paper contains a detailed derivation of results first announced in arXiv:1403.4543.

arXiv comment76 pages. 2 figures. v2: added references and fixed some typos

References in corpus (99)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• The Black Hole in Three Dimensional Space Time
• Microscopic Origin of the Bekenstein-Hawking Entropy
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Geometry of the 2+1 Black Hole
• Black Hole Entropy from Near-Horizon Microstates
• Review of AdS/CFT Integrability: An Overview
• The D1/D5 System And Singular CFT
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Bethe Ansatz for Quantum Strings
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Classical/quantum integrability in AdS/CFT
• Giant Magnons
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Foundations of the AdS_5 x S^5 Superstring. Part I
• Integrability for the Full Spectrum of Planar AdS/CFT II
• Integrability for the Full Spectrum of Planar AdS/CFT
• Spin chains and string theory
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Integrability and the AdS(3)/CFT(2) correspondence
• A Construction of Killing Spinors on S^n
• On String S-matrix, Bound States and TBA
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• String hypothesis for the AdS_5 x S^5 mirror
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• Large N=4 Holography
• The Holographic Dual of AdS3 x S3 x S3 x S1
• The SU(3) spin chain sigma model and string theory
• Worldsheet Scattering in AdS_5 x S^5
• Domain Walls from Anti-de Sitter Spacetime
• Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector
• The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
• On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
• Strings on Semisymmetric Superspaces
• Green-Schwarz Strings in TsT-transformed backgrounds
• A dynamic su(1|1)^2 S-matrix for AdS3/CFT2
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• String Theory on AdS_3
• Extended Y-system for the $Ad{S}_5/CF{T}_4$ correspondence
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• On the Hopf algebra structure of the AdS/CFT S-matrix
• T-Duality in the Green-Schwarz Formalism, and the Massless/Massive IIA Duality Map
• Integrability, spin-chains and the AdS3/CFT2 correspondence
• All-loop Bethe ansatz equations for AdS3/CFT2
• Proving the PP-Wave/CFT_2 Duality
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Dressing phases of AdS3/CFT2
• Giant magnons in the D1-D5 system
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• A Spin Chain for the Symmetric Product CFT_2
• String Theory on AdS_3 x S^3 x S^3 x S^1
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• PP-Wave / CFT_2 Duality
• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• Worldsheet scattering in AdS(3)/CFT(2)
• The Dressing Factor and Crossing Equations
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Comments On String Theory
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• The GS String Action on AdS(3)xS(3) with Ramond-Ramond Charge
• Massless Flows II: the exact S-matrix approach
• S-matrix for magnons in the D1-D5 system
• The Search for a Holographic Dual to AdS(3)xS(3)xS(3)xS(1)
• Integrability of the AdS_5 x S^5 superstring and its deformations
• 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
• Massless Flows I: the sine-Gordon and O(n) models
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Super spin chain coherent state actions and $Ad{S}_5\times S^5$ superstring
• Yangians, S-matrices and AdS/CFT
• Superparticle and superstring in AdS_3 x S^3 Ramond-Ramond background in light-cone gauge
• Spinning strings and minimal surfaces in $Ad{S}_3$ with mixed 3-form fluxes
• Finiteness and Unitarity of Lorentz-Covariant Green-Schwarz Superstring Amplitudes
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• Quantum corrections to short folded superstring in AdS_3 x S^3 x M^4
• Brane intersections, anti-de Sitter spacetimes and dual superconformal theories
• Generalized unitarity and the worldsheet S matrix in AdS_n x S^n x M^(10-2n)
• The type II superstring to order theta^4
• String solutions in AdS_3 x S^3 x T^4 with NS-NS B-field
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• Spiky strings on AdS3 x S3 with NS-NS flux
• The low energy limit of the AdS(3) x S(3) x M(4) spinning string
• Classical integrability in the BTZ black hole
• Massless integrable quantum field theories and massless scattering in 1+1 dimensions
• Generating string solutions in BTZ

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