Foundations of the AdS_5 x S^5 Superstring. Part I

Abstract

We review the recent advances towards finding the spectrum of the AdS_5 x S^5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present Part I deals with foundations of classical string theory in AdS_5 x S^5, light-cone perturbative quantization and derivation of the exact light-cone world-sheet scattering matrix.

161 pages

References in corpus (29)

• 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
• Integrability for the Full Spectrum of Planar AdS/CFT II
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Finite-size Effects from Giant Magnons
• Quantum corrections to the string Bethe ansatz
• 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
• On AdS_5 x S^5 String S-matrix
• Magnon Bound States and the AdS/CFT Correspondence
• Wrapping at four loops in N=4 SYM
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Wrapping interactions at strong coupling -- the giant magnon
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• On the Hopf algebra structure of the AdS/CFT S-matrix
• The S-matrix of String Bound States
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Complete 1-loop test of AdS/CFT
• A Universality Test of the Quantum String Bethe Ansatz
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Exact expressions for quantum corrections to spinning strings
• The magnon kinematics of the AdS/CFT correspondence
• The Four-Loop Dressing Phase of N=4 SYM
• World-sheet scattering in AdS_5 x S^5 at two loops
• Constructing the AdS/CFT dressing factor
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Factorized world-sheet scattering in near-flat AdS_5 x S^5

Cited by in corpus (255)

• Review of AdS/CFT Integrability: An Overview
• An integrable deformation of the AdS_5 x S^5 superstring action
• Integrability for the Full Spectrum of Planar AdS/CFT II
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• Scattering into the fifth dimension of N=4 super Yang-Mills
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Abelian Yang-Baxter Deformations and TsT transformations
• 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
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• 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
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• A dynamic su(1|1)^2 S-matrix for AdS3/CFT2
• Exacting N=4 Superconformal Symmetry
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• Integrable deformations of T-dual $\sigma$ models
• Integrability of classical strings dual for noncommutative gauge theories
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• All-loop Bethe ansatz equations for AdS3/CFT2
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Dressing phases of AdS3/CFT2
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• A Spin Chain for the Symmetric Product CFT_2
• On $T\bar{T}$ deformations and supersymmetry
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• A Jordanian deformation of AdS space in type IIB supergravity
• 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
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Worldsheet scattering in AdS(3)/CFT(2)
• The Dressing Factor and Crossing Equations
• Superstrings in AdS(2)xS(2)xT(6)
• Almost abelian twists and AdS/CFT
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• Integrable Deformations of Sigma Models
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Structure constants at wrapping order
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• The Quantum Deformed Mirror TBA I
• Two-dimensional S-matrices from unitarity cuts
• Konishi operator at intermediate coupling
• On (non)integrability of classical strings in p-brane backgrounds
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Double Wick rotating Green-Schwarz strings
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• The one-loop worldsheet S-matrix for the AdS(n) x S(n) x T(10-2n) superstring
• Integrability of Green-Schwarz Sigma Models with Boundaries
• Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• The spectral problem for strings on twisted AdS_5 x S^5
• Quantum integrability and functional equations
• $T\bar{T}$ deformations and integrable spin chains
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Introduction to the thermodynamic Bethe ansatz
• Quantum AdS_5 x S^5 superstring in the AdS light-cone gauge
• Temperature quantization from the TBA equations
• Flow equations for generalised $T\bar{T}$ deformations
• Quantum deformations of the flat space superstring
• Generalized IIB supergravity from exceptional field theory
• On Yangian Symmetry in Planar N=4 SYM
• $T\bar{T}$ deformations as TsT transformations
• The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills
• Deformed Neumann model from spinning strings on (AdS_5 x S^5)_η
• A light-cone approach to three-point functions in AdS_5 x S^5
• Yangians, S-matrices and AdS/CFT
• 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
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• A Quantum Affine Algebra for the Deformed Hubbard Chain
• Yang-Baxter and the Boost: splitting the difference
• Local $\beta$-deformations and Yang-Baxter sigma model
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality
• Haldane limits via Lagrangian embeddings
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• New Dressing Factors for AdS3/CFT2
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux
• The Chern-Simons Origin of Superstring Integrability
• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• 4-dimensional Chern-Simons theory and integrable field theories
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• Worldsheet Form Factors in AdS/CFT
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Superstrings in AdS
• Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory
• A Relativistic Relative of the Magnon S-Matrix
• General phase spaces: from discrete variables to rotor and continuum limits
• Superintegrability of Geodesic Motion on the Sausage Model
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• Hamiltonian dynamics and the hidden symmetries of the AdS_5 x S^5 superstring
• Hybrid-NLIE for the AdS/CFT spectral problem
• Unimodular jordanian deformations of integrable superstrings
• Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators
• Lectures on S-matrices and Integrability
• AdS_4 x CP^3 superstring in the light-cone gauge
• Yangian symmetry of the Y=0 maximal giant graviton
• The AdS(n) x S(n) x T(10-2n) BMN string at two loops
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• 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
• Introduction to classical and quantum integrability
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• Light-cone gauge Hamiltonian for AdS_4 x CP^3 superstring
• Comments on the Mirror TBA
• TTbar deformation and the light-cone gauge
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Harmonic Superspace from the $Ad{S}_5\times S^5$ Pure Spinor Formalism
• The S-matrix algebra of the AdS2 X S2 superstring
• Comments on World-Sheet Form Factors in AdS/CFT
• Massless S matrices for AdS3/CFT2
• The worldsheet low-energy limit of the AdS_4 x CP^3 superstring
• Integrable asymmetric $\lambda$-deformations
• Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Integrability of the eta-deformed Neumann-Rosochatius model
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• Positivity of hexagon perturbation theory
• Massless sector of AdS_3 superstrings: a geometric interpretation
• Universal blocks of the AdS/CFT Scattering Matrix
• Integrable Superstrings on the Squashed Three-sphere
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
• The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
• Integrable achiral D5-brane reflections and asymptotic Bethe equations
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Classifying integrable symmetric space strings via factorized scattering
• The plane-wave spectrum from the worldsheet
• D1 and D5-brane giant gravitons on $Ad{S}_3\times S^3\times S^3\times S^1$
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• An improved AFS phase for AdS3 string integrability
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Integrable strings for AdS/CFT
• Bonus Symmetry for Super Wilson Loops
• On the Spectrum of the AdS_5xS^5 String at large lambda
• Lifting asymptotic degeneracies with the Mirror TBA
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• Coset space actions for nonrelativistic strings
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory
• On the quantization of continuous non-ultralocal integrable systems
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• Chaotic spin chains in AdS/CFT
• Worldsheet S-matrix of beta-deformed SYM
• Bound States in the Mirror TBA
• On the reflection of magnon bound states
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Extending the non-relativistic string AdS coset
• Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Exact Quantization of a Superparticle in AdS_5 x S^5
• Quasi-local formulation of the mirror TBA
• Integrable deformations of AdS/CFT
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• Open-closed superstring amplitudes using vertex operators in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Non Relativistic Limit of Integrable QFT with fermionic excitations
• Generalized Dualities and Supergroups
• Static Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• Giant Magnons of String Theory in the Lambda Background
• Nonlocal Symmetries and Factorized Scattering
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• Semiclassical equivalence of Green-Schwarz and Pure-Spinor/Hybrid formulations of superstrings in AdS(5) x S(5) and AdS(2) x S(2) x T(6)
• Yang-Baxter deformations of $W_{2,4}\times T^{1,1}$ and the associated T-dual models
• $Ad{S}_5\times S^5$ supergravity vertex operators
• Non-relativistic string monodromies
• Two-loop corrections to partition function of Pohlmeyer-reduced theory for AdS_5 x S^5 superstring
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• Spectral curve for open strings attached to the Y=0 brane
• Lax pairs for string Newton Cartan geometry
• Three-point functions at strong coupling in the BMN limit
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Light-Cone Gauge in Non-Relativistic AdS${}_5\times$S${}^5$ String Theory
• Off-shell symmetry algebra of the AdS_4 x CP^3 superstring
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• Boost generator in AdS_3 integrable superstrings for general braiding
• Thermodynamics of the quantum $su(1,1)$ Landau-Lifshitz model
• Integrability and the Conformal Field Theory of the Higgs branch
• On the massless modes of the AdS3/CFT2 integrable systems
• Integrability treatment of AdS/CFT orbifolds
• Coset construction of AdS particle dynamics
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Reflection algebra, Yangian symmetry and bound-states in AdS/CFT
• Drinfeld basis for string-inspired Baxter operators
• Integrability of D1-brane on Group Manifold
• Free field representation of the ZF algebra of the SU(N)xSU(N) PCF model
• SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence
• Probing $\eta$ deformed backgrounds with $Dp$ branes
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• New Formulation of the Type IIB Superstring Action in $Ad{S}_5\times S^5$
• A perturbative approach to the non-relativistic string spectrum
• Bethe Ansatz for Quantum-Deformed Strings
• Note About Integrability of Non-Relativistic String
• Lax pairs on Yang-Baxter deformed backgrounds
• Wrapping effects in supersymmetric gauge theories
• Vertex operators for the plane wave pure spinor string
• Consistent bilinear Wess-Zumino term for open AdS superstring
• On Semiclassical Equivalence of Green-Schwarz and Pure Spinor Strings in AdS(5) x S(5)
• Holography on the lattice: the string worldsheet perspective
• Integrability structures in string theory
• The plane-wave limit of ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• Fermionic reductions of the AdS4 x CP3 superstring
• Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$
• Recent Trends in Superstring Phenomenology
• Geometry of Massless Scattering in Integrable Superstring
• Newton-Cartan $D0$ branes from $D1$ branes and integrability
• Extensive numerical study of a D-brane, anti-D-brane system in AdS5/CFT4
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons and Mirror Symmetry
• Bound State Scattering Simplified
• Remarks on the geometrical properties of semiclassically quantized strings
• Lee-Yang Model in Presence of Defects
• Superembedding approach to superstring in AdS(5)xS*5 superspace
• Vacuum type space-like string surfaces in AdS_3 x S^3
• Canonical Analysis of New Non-Relativistic String Action and Uniform Light-Cone Gauge Formulation
• New Non-Relativistic String in AdS(5)xS(5)
• WZNW Strings, Unitarity and Anti de Sitter spaces
• Unitarity methods for scattering in two dimensions
• Note About Hamiltonian Dynamics of String in Non-Relativistic D3-Brane Background
• On exactly solvable Yang-Baxter models and enhanced symmetries
• On the algebraic curves for circular and folded strings in ${\text{AdS}}_5\times S^5$
• On non-canonical degrees of freedom
• On the singularities of the R-R AdS_3 x S^3 x T^4 S matrix
• Einstein metrics on homogeneous superspaces
• Tenfold Way for Holography : AdS/CFT and Beyond
• Uniform Gauge for D1-brane in General Background
• Canonical Description of T-duality for Fundamental String and D1-Brane and Double Wick Rotation
• Transfer matrices for AdS3/CFT2