A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations

Abstract

A generalization of the Yang-Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in involution which form the Cartan sub-algebra of the braided quantum group. Representations diagonalizing these operators are described through relying on an easy generalization of Algebraic Bethe Ansatz techniques. The conjecture that this monodromy matrix algebra leads, {\it in the cylinder continuum limit}, to a Perturbed Minimal Conformal Field Theory description is analysed and supported.

Latex file, 46 pages

Cited by in corpus (19)

• Integrability of the AdS_5 x S^5 superstring and its deformations
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
• The generalized non-linear Schrodinger model on the interval
• The open XXZ and associated models at q root of unity
• Integrability from 2d N=(2,2) Dualities
• Exact conserved quantities on the cylinder I: conformal case
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Integrable aspects of the scaling q-state Potts models II: finite-size effects
• Exact conserved quantities on the cylinder II: off-critical case
• Inhomogeneous Heisenberg Spin Chain and Quantum Vortex Filament as Non-Holonomically Deformed NLS Systems
• On the Integrable Structure of the Ising Model
• Integrability of two-species partially asymmetric exclusion processes
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• Commuting quantum traces: the case of reflection algebras
• Note on Nonlinear Schrödinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs Theory
• Ultralocal solutions for quantum integrable nonultralocal models
• Freidel-Maillet type presentations of $U_q(s{l}_2)$