Integrability of the AdS_5 x S^5 superstring and its deformations

Abstract

This article reviews the application of integrability to the spectral problem of strings on AdS_5 x S^5 and its deformations. We begin with a pedagogical introduction to integrable field theories culminating in the description of their finite-volume spectra through the thermodynamic Bethe ansatz. Next, we apply these ideas to the AdS_5 x S^5 string and in later chapters discuss how to account for particular integrable deformations. Through the AdS/CFT correspondence this gives an exact description of anomalous scaling dimensions of single trace operators in planar N=4 supersymmetry Yang-Mills theory, its `orbifolds', and beta and gamma-deformed supersymmetric Yang-Mills theory. We also touch upon some subtleties arising in these deformed theories. Furthermore, we consider complex excited states (bound states) in the su(2) sector and give their thermodynamic Bethe ansatz description. Finally we discuss the thermodynamic Bethe ansatz for a quantum deformation of the AdS_5 x S^5 superstring S-matrix, with close relations to among others Pohlmeyer reduced string theory, and briefly indicate more recent developments in this area.

v3, published version, introduction slightly broadened, typos corrected, updates to outlook and references. Review based on author's PhD thesis, 214 pages, many figures. Partly based on arXiv:1009.4118, arXiv:1103.5853, arXiv:1111.0564, arXiv:1201.1451, arXiv:1208.3478, and arXiv:1210.8185

References in corpus (46)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• An integrable deformation of the AdS_5 x S^5 superstring action
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• Jordanian deformations of the AdS_5xS^5 superstring
• 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
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Magnon Bound States and the AdS/CFT Correspondence
• Wrapping at four loops in N=4 SYM
• Quantum Deformations of the One-Dimensional Hubbard Model
• On the Singularities of the Magnon S-matrix
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• The S-matrix of String Bound States
• Integrability of classical strings dual for noncommutative gauge theories
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• The Quantum Deformed Mirror TBA I
• Konishi operator at intermediate coupling
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• Finite-size effects in the superconformal beta-deformed N=4 SYM
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• theta_C from the Dihedral Flavor Symmetries D_7 and D_14
• Integrable twists in AdS/CFT
• Screening effects on meson masses from holography
• Chiral gauge dynamics and dynamical supersymmetry breaking
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM
• Coordinate Bethe Ansatz for the String S-Matrix
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Perturbative study of the transfer matrix on the string worldsheet in AdS(5)xS(5)
• Six-loop Konishi anomalous dimension from the Y-system
• Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory
• Minimal solution of the AdS/CFT crossing equation
• A next-to-leading Luescher formula
• Instantons and Emergent AdS_3 x S^3 Geometry
• On the $Ad{S}_5/CF{T}_4$ TBA and its analytic properties
• Orbifolded Konishi from the Mirror TBA
• Symplectic Deformations of Integrable Field Theories and AdS/CFT
• A review of integrable deformations in AdS/CFT
• Counting charged massless states in the (0,2) heterotic CFT/geometry connection

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• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
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• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• From Interacting Particles to Equilibrium Statistical Ensembles
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Towards integrability for AdS3/CFT2
• Almost abelian twists and AdS/CFT
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Lectures on the Bethe Ansatz
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Introduction to the thermodynamic Bethe ansatz
• Deformed Neumann model from spinning strings on (AdS_5 x S^5)_η
• On jordanian deformations of AdS_5 and supergravity
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• Integrability of the eta-deformed Neumann-Rosochatius model
• Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Chaotic spin chains in AdS/CFT
• Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion
• ABJM quantum spectral curve and Mellin transform
• Chaos Bound and its violation in Black p-brane
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• Circular string in a Black p-brane leading to chaos
• Open Spin Chains from Determinant Like Operators in ABJM Theory
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Fast spinning strings on $\eta$ deformed $Ad{S}_5\times S^5$
• Y-system for $\gamma$-deformed ABJM Theory
• Integrability of D1-brane on Group Manifold with Mixed Three Form Flux
• Integrability treatment of AdS/CFT orbifolds
• Integrability of Orbifold ABJM Theories
• Probing $\eta$ deformed backgrounds with $Dp$ branes
• Integrability of D1-brane on Group Manifold
• Marginal deformations and quasi-Hopf algebras
• Integrable Hopf twists, marginal deformations and generalised geometry
• Polyvector deformations of Type IIB backgrounds
• On type 0 string theory in solvable RR backgrounds
• Spin chains and classical strings in two parameters $q$-deformed AdS${}_3\times$S${}^3$
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• On analytical perturbative solution of ABJM quantum spectral curve
• Integrability structures in string theory
• Spectral curve for gamma-deformed AdS/CFT
• Transfer matrices for AdS3/CFT2
• Uniform Gauge for D1-brane in General Background