Introduction to Yangian symmetry in integrable field theory

Abstract

Three introductory lectures: on Yangians and their representations; on Yangian symmetry in 1+1D integrable (bulk) field theory; and on the effect of a boundary upon this symmetry.

Lectures given at 'String theory in curved backgrounds and boundary conformal field theory', Erwin Schroedinger Instutute, Vienna, June 2004. References added in v4

References in corpus (48)

• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Open Strings and D-branes in WZNW model
• D-branes in group manifolds
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• An Introduction to Yangian Symmetries
• The Yangian symmetry of the Hubbard Model
• Dressing Symmetries
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
• Coideal Subalgebras and Quantum Symmetric Pairs
• Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]
• Analytic Bethe Ansatz for Fundamental Representations of Yangians
• Boundary remnant of Yangian symmetry and the structure of rational reflection matrices
• The gl(M|N) Super Yangian and Its Finite Dimensional Representations
• Yangian Symmetry in Conformal Field Theory
• Representations of reflection algebras
• Yangians, Integrable Quantum Systems and Dorey's rule
• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• On a class of representations of the Yangian and moduli space of monopoles
• Conserved charges and supersymmetry in principal chiral and WZW models
• Exact Yangian Symmetry in the Classical Euler-Calogero-Moser Model
• Rational K-matrices and representations of twisted Yangians
• Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line
• Boundary scattering, symmetric spaces and the principal chiral model on the half-line
• On the Yangian Y(e_8) quantum symmetry of maximal supergravity in two dimensions
• Yangian Double and Rational R-matrix
• Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy
• Yangian symmetry in the Non Linear Schrodinger hierarchy
• Quantum, higher-spin, local charges in symmetric space sigma models
• Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)xSO(n) and Sp(2n)/Sp(n)xSp(n)
• On Symmetries of Some Massless 2D Field Theories
• Logarithmic Yangians in WZW models
• Classically integrable boundary conditions for symmetric-space sigma models
• Form factors for principal chiral field model with Wess-Zumino-Novikov-Witten term
• Yangians and their applications
• Combinatorial Structure of Finite Dimensional Representations of Yangians: the Simply-Laced Case
• Hopf structure of the Yangian Y(sl_n) in the Drinfel'd realisation
• Multi-parameter deformed and nonstandard $Y(g{l}_M)$ Yangian symmetry in a novel class of spin Calogero-Sutherland models
• Fusion, mass, and representation theory of the Yangian algebra
• R-matrices and Tensor Product Graph Method
• Lattice quantization of Yangian charges
• Algebraic Proof of the Symmetric Space Theorem
• Non-Linear Sigma Models on a Half Plane
• Representations of Yangians associated with skew Young diagrams
• Systematic proof of the existence of Yangian symmetry in chiral Gross-Neveu models
• Boundary scattering in the SU(N) principal chiral model on the half-line with conjugating boundary conditions
• A remarkable connection between Yangians and finite W-algebras
• Exact Zero Temperature Correlation Functions for Two-Leg Hubbard Ladders and Carbon Nanotubes

Cited by in corpus (87)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Superuniversality of superdiffusion
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• The WZNW model on PSU(1,1|2)
• Brane Partons and Singleton Strings
• Non-local charges, Zm gradings and coset space actions
• Lectures on Yangian Symmetry
• Integrable Deformations of Sigma Models
• The Algebra of Transition Matrices for the AdS_5 x S^5 Superstring
• Classical Open String Integrability
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Yangians, S-matrices and AdS/CFT
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Boundary Spectra in Superspace Sigma-Models
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
• Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
• On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions
• A dictionary between R-operators, on-shell graphs and Yangian algebras
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
• Equivalences between three presentations of orthogonal and symplectic Yangians
• Yangian symmetry of the Y=0 maximal giant graviton
• Spin Models and Superconformal Yang-Mills Theory
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains
• Yangian Bootstrap for Massive Feynman Integrals
• Cooper pairs and exclusion statistics from coupled free-fermion chains
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Affine q-deformed symmetry and the classical Yang-Baxter sigma-model
• Twisted Yangians for symmetric pairs of types B, C, D
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Massive Fishnets
• Secret Symmetries in AdS/CFT
• Integrable QFT and Longo-Witten endomorphisms
• Achiral boundaries and the twisted Yangian of the D5-brane
• Representations of twisted Yangians of types B, C, D: I
• Universal blocks of the AdS/CFT Scattering Matrix
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Yangian symmetry of boundary scattering in AdS/CFT and the explicit form of bound state reflection matrices
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices
• On the reflection of magnon bound states
• Integrability for Feynman Integrals
• Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions
• Gauge Theory and Boundary Integrability
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• Nonlocal Symmetries and Factorized Scattering
• Yangian in the Twistor String
• Representations of twisted Yangians of types B, C, D: II
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz
• Yangian Symmetry in N=4 super Yang-Mills
• The secret symmetries of the AdS/CFT reflection matrices
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• The Yangian of sl(n|m) and the universal R-matrix
• Drinfeld J Presentation of Twisted Yangians
• Kac-Moody and Virasoro Symmetries of Principal Chiral Sigma Models
• Yangians in Deformed Super Yang-Mills Theories
• Reflection algebra, Yangian symmetry and bound-states in AdS/CFT
• Drinfeld basis for string-inspired Baxter operators
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Modified AKNS model, Riccati-type pseudo-potential approach and infinite towers of quasi-conservation laws
• Yangian Superalgebras in Conformal Field Theory
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• From Twisted Quantum Loop Algebras to Twisted Yangians
• New boundary monodromy matrices for classical sigma models
• Conserved Charges in the Principal Chiral Model on a Supergroup
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• The particle-hole transformation, supersymmetry and achiral boundaries of the open Hubbard model
• Algebraic K-Theory and Partition Functions in Conformal Field Theory
• Boundary Perimeter Bethe Ansatz
• Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries
• Killing scalar of non-linear sigma models on G/H realizing the classical exchange algebra
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Twisted Yangian symmetry of the open Hubbard model
• 6D dual superconformal algebra
• Wilson Loops and Integrability
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes