An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction

Abstract

We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series.

arXiv commentv2, published version

References in corpus (46)

• Gauge Theory Correlators from Non-Critical String Theory
• The World as a Hologram
• Review of AdS/CFT Integrability: An Overview
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• The su(2|2) Dynamic S-Matrix
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• High energy QCD as a completely integrable model
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Integrability for the Full Spectrum of Planar AdS/CFT II
• The su(2|3) Dynamic Spin Chain
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Quantum spectral curve for AdS_5/CFT_4
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Thermodynamic Bubble Ansatz
• Excited states by analytic continuation of TBA equations
• Integrable Quantum Field Theories in Finite Volume: Excited State Energies
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Introduction to Yangian symmetry in integrable field theory
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• An Introduction to Yangian Symmetries
• Towards integrability for AdS3/CFT2
• Wrapping interactions and the genus expansion of the 2-point function of composite operators
• Lectures on Yangian Symmetry
• Lectures on the Bethe Ansatz
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Introduction to the thermodynamic Bethe ansatz
• On Yangian Symmetry in Planar N=4 SYM
• Yangians, S-matrices and AdS/CFT
• Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states
• Alleviating the non-ultralocality of the AdS_5 x S^5 superstring
• Lectures on S-matrices and Integrability
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• Integrability and the AdS/CFT correspondence
• First-principles derivation of the AdS/CFT Y-systems
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities

Cited by in corpus (38)

• Abelian Yang-Baxter Deformations and TsT transformations
• Integrable deformations of T-dual $\sigma$ models
• Almost abelian twists and AdS/CFT
• $T\bar{T}$ deformations and integrable spin chains
• Introduction to the thermodynamic Bethe ansatz
• Flow equations for generalised $T\bar{T}$ deformations
• Tensorial Gross-Neveu models
• The Chern-Simons Origin of Superstring Integrability
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Unimodular jordanian deformations of integrable superstrings
• The Hagedorn temperature of AdS5/CFT4 via integrability
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Condition on Ramond-Ramond fluxes for factorization of worldsheet scattering in anti-de Sitter space
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Chaotic spin chains in AdS/CFT
• Constraining integrable AdS/CFT with factorized scattering
• Chaos Bound and its violation in Black p-brane
• ABJM quantum spectral curve and Mellin transform
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Analytic Non-Integrability and S-Matrix Factorization
• The twisted story of worldsheet scattering in $\eta$-deformed $Ad{S}_5\times S^5$
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Coset construction of AdS particle dynamics
• SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence
• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
• Spin chains and classical strings in two parameters $q$-deformed AdS${}_3\times$S${}^3$
• Deterministic Chaos vs Integrable Models
• On analytical perturbative solution of ABJM quantum spectral curve
• Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$
• Investigating (Non)-Integrability and Pulsating String in D3-Brane Background
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• On exactly solvable Yang-Baxter models and enhanced symmetries
• Vacuum configuration of winding superstrings from non-standard semiclassical quantization