$A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited

Abstract

Generic classically integrable boundary conditions for the $A_n^{(1)}$ affine Toda field theories (ATFT) are investigated. The present analysis rests primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the $A_2^{(1)}$ ATFT, however our results may be generalized for any $A_n^{(1)}$ ($n>1$). We assume here two distinct types of boundary conditions called some times soliton preserving (SP), and soliton non-preserving (SNP) associated to two distinct algebras, i.e. the reflection algebra and the ($q$) twisted Yangian respectively. The boundary local integrals of motion are then systematically extracted from the asymptotic expansion of the associated transfer matrix. In the case of SNP boundary conditions we recover previously known results. The other type of boundary conditions (SP), associated to the reflection algebra, are novel in this context and lead to a different set of conserved quantities that depend on free boundary parameters. It also turns out that the number of local integrals of motion for SP boundary conditions is `double' compared to those of the SNP case.

arXiv comment26 pages, Latex. Typos corrected

References in corpus (44)

• Gauge Theory Correlators from Non-Critical String Theory
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Classical/quantum integrability in AdS/CFT
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Classically integrable boundary conditions for affine Toda field theories
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Affine Toda field theory on a half line
• Factorized Scattering in the Presence of Reflecting Boundaries
• Classical/quantum integrability in non-compact sector of AdS/CFT
• Analytical Bethe Ansatz for Quantum-Algebra-Invariant Spin Chains
• Reflecting magnons
• Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line
• Exact solution of the $S{U}_q(n)$ invariant quantum spin chains
• Coideal subalgebras in quantum affine algebras
• Affine Toda Field Theory in the Presence of Reflecting Boundaries
• Boundary remnant of Yangian symmetry and the structure of rational reflection matrices
• Conformal Fixed Points of Unidentified Gauge Theories
• General boundary conditions for the sl(N) and sl(M|N) open spin chains
• Bulk and Boundary S Matrices for the SU(N) Chain
• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
• Quantum spin chain with "soliton non-preserving" boundary conditions
• Spectrum and Bethe ansatz equations for the U_ {q}(gl(N)) closed and open spin chains in any representation
• Rational K-matrices and representations of twisted Yangians
• Analytical Bethe Ansatz for $A_{2n-1}^{(2)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ quantum-algebra-invariant open spin chains
• Duality and quantum-algebra symmetry of the A_{N-1}^(1) open spin chain with diagonal boundary fields
• From affine Hecke algebras to boundary symmetries
• Non-diagonal solutions to reflection equations in $su(n)$ spin chains
• Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• Coupling integrable field theories to mechanical systems at the boundary
• The generalized non-linear Schrodinger model on the interval
• The Highest Weight Property for the $S{U}_q(n)$ Invariant Spin Chains
• Integrable boundary conditions for classical sine-Gordon theory
• On a_2^(1) Reflection Matrices and Affine Toda Theories
• Quantum integrability in two-dimensional systems with boundary
• Soliton-preserving boundary condition in affine Toda field theories
• On reflection algebras and twisted Yangians
• Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model
• Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions
• Background field boundary conditions for affine Toda field theories
• (Quantum) twisted Yangians: symmetry, Baxterisation and centralizers

Cited by in corpus (10)

• Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
• Sigma models in the presence of dynamical point-like defects
• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• Quantum line operators from Lax pairs
• Jumps and twists in affine Toda field theories
• New reflection matrices for the U_q(gl(m|n)) case
• Infinite dimension reflection matrices in the sine-Gordon model with a boundary
• Generalized Landau-Lifshitz models on the interval
• Scattering matrices in the sl(3) twisted Yangian
• Real Hamiltonian forms of affine Toda field theories: spectral aspects