On String S-matrix, Bound States and TBA

Abstract

The study of finite J effects for the light-cone AdS superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The S-matrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror S-matrix fixes the S-matrices of both theories essentially uniquely. The resulting string S-matrix S(z_1,z_2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2^{M-1} solutions of the M-particle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they might receive a finite J correction to their energy which is complex, or the energy correction might exceed corrections arising due to finite J modifications of the Bethe equations thus making the asymptotic Bethe ansatz inapplicable.

77 pages, 6 figures, v2: the statement about the periodicity condition for mirror fermions corrected; typos corrected; references added, v3: misprints corrected

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• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Bethe Ansatz for Quantum Strings
• Classical/quantum integrability in AdS/CFT
• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• 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
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Finite-size Effects from Giant Magnons
• Quantum corrections to the string Bethe ansatz
• Excited states by analytic continuation of TBA equations
• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• On AdS_5 x S^5 String S-matrix
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Magnon Bound States and the AdS/CFT Correspondence
• On Quantum Corrections to Spinning Strings and Bethe Equations
• On the highest transcendentality in N=4 SUSY
• On the Singularities of the Magnon S-matrix
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
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• On the Hopf algebra structure of the AdS/CFT S-matrix
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
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• Exact expressions for quantum corrections to spinning strings
• How Accurate is the Quantum String Bethe Ansatz?
• New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5
• The magnon kinematics of the AdS/CFT correspondence
• World-sheet scattering in AdS_5 x S^5 at two loops
• Constructing the AdS/CFT dressing factor
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
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Cited by in corpus (147)

• 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
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• Exact AdS/CFT spectrum: Konishi dimension at any coupling
• On deformations of AdS_n x S^n supercosets
• String hypothesis for the AdS_5 x S^5 mirror
• T-systems and Y-systems in integrable systems
• Four loop twist two, BFKL, wrapping and strings
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Quantum Deformations of the One-Dimensional Hubbard Model
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Strings on NS-NS Backgrounds as Integrable Deformations
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Five loop Konishi from AdS/CFT
• Integrable Wilson loops
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• 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
• The S-matrix of String Bound States
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Dressing phases of AdS3/CFT2
• Long-Range Deformations for Integrable Spin Chains
• Five-loop Konishi from the Mirror TBA
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• The Dressing Factor and Crossing Equations
• Conserved currents and $\text{T}{\bar{\text{T}}}_s$ irrelevant deformations of 2D integrable field theories
• Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Exploring the mirror TBA
• Y-system and Quasi-Classical Strings
• Twist-three at five loops, Bethe Ansatz and wrapping
• Finite-Size Effects for Dyonic Giant Magnons
• Protected string spectrum in AdS3/CFT2 from worldsheet integrability
• Magnon dispersion to four loops in the ABJM and ABJ models
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• The Quantum Deformed Mirror TBA I
• Wronskian Solution for AdS/CFT Y-system
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• Konishi operator at intermediate coupling
• Quantum Wrapped Giant Magnon
• Double Wick rotating Green-Schwarz strings
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Finite size effects for giant magnons on physical strings
• 5-loop Konishi from linearized TBA and the XXX magnet
• The spectral problem for strings on twisted AdS_5 x S^5
• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• $T\bar{T}$ deformations and integrable spin chains
• Twisting the Mirror TBA
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• The Quantum Deformed Mirror TBA II
• Quantum deformations of the flat space superstring
• Temperature quantization from the TBA equations
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• Flow equations for generalised $T\bar{T}$ deformations
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Twisted Bethe equations from a twisted S-matrix
• Yangians, S-matrices and AdS/CFT
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• 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
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• New Dressing Factors for AdS3/CFT2
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• The Bajnok-Janik formula and wrapping corrections
• Interacting finite-size magnons
• Discrete Hirota dynamics for AdS/CFT
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• Boundary state bootstrap and asymptotic overlaps in AdS/dCFT
• An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
• Comments on the Boundary Scattering Phase
• Hybrid-NLIE for the AdS/CFT spectral problem
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
• Computing Three-Point Functions for Short Operators
• Review of AdS/CFT Integrability, Chapter III.5: Luscher corrections
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons
• The spectrum of tachyons in AdS/CFT
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Comments on the Mirror TBA
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• Minimal solution of the AdS/CFT crossing equation
• Exceptional Operators in N=4 super Yang-Mills
• Massless S matrices for AdS3/CFT2
• Fusion hierarchies for N = 4 superYang-Mills theory
• A next-to-leading Luescher formula
• Y-system for Y=0 brane in planar AdS/CFT
• Wrapping in maximally supersymmetric and marginally deformed N=4 Yang-Mills
• Universal blocks of the AdS/CFT Scattering Matrix
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Finite size effect on the magnon's correlation functions
• Fermionic Correlators from Integrability
• Structure of the string R-matrix
• Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
• Yangian symmetry of boundary scattering in AdS/CFT and the explicit form of bound state reflection matrices
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• A general definition of $J{T}_a$ -- deformed QFTs
• Integrable bootstrap for AdS3/CFT2 correlation functions
• On the Spectrum of the AdS_5xS^5 String at large lambda
• Lifting asymptotic degeneracies with the Mirror TBA
• The Bethe Ansatz for AdS5 x S5 Bound States
• Konishi at strong coupling from ABE
• Bound States in the Mirror TBA
• On the reflection of magnon bound states
• Y-system for Z_S Orbifolds of N=4 SYM
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Exactly solvable many-body dynamics from space-time duality
• Quasi-local formulation of the mirror TBA
• Orbifolded Konishi from the Mirror TBA
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix
• Three-point functions at strong coupling in the BMN limit
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• Integrability treatment of AdS/CFT orbifolds
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Wrapping corrections for non-diagonal boundaries in AdS/CFT
• Wrapping effects in supersymmetric gauge theories
• Contour deformation trick in hybrid NLIE
• Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
• Quantum deformation of cubic string field theory
• Operator mixing in N = 4 SYM: The Konishi anomaly re-re-visited
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Fusion for AdS/CFT boundary S-matrices
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• Large spin expansion of the wrapping correction to Freyhult-Rej-Zieme twist operators
• Transfer matrices for AdS3/CFT2
• Deforming integrable models of AdS${}_3$ strings
• Canonical Description of T-duality for Fundamental String and D1-Brane and Double Wick Rotation