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

TL;DR

This paper introduces a braided Yang-Baxter algebra for coupled lattice quantum KdV equations, exploring its algebraic properties, representations via algebraic Bethe Ansatz, and potential continuum limit connections to perturbed minimal conformal field theories.

Contribution

It generalizes the Yang-Baxter algebra to coupled lattice quantum KdV systems, providing new algebraic structures and representation methods, and investigates their continuum limit implications.

Findings

Braided Yang-Baxter algebra for coupled lattice quantum KdV established

Representations constructed using generalized Algebraic Bethe Ansatz

Support for continuum limit leading to perturbed minimal conformal field theory

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.