Integrable structure of $\textrm{BCD}$ conformal field theory and boundary Bethe ansatz for affine Yangian

TL;DR

This paper explores the integrable structures of BCD symmetric conformal field theories by representing them as affine Yangian spin chains with boundaries, deriving Bethe ansatz equations for their spectra.

Contribution

It introduces boundary solutions to the Sklyanin KRKR equation compatible with affine Yangian R-matrices, advancing the understanding of boundary integrable models in CFT.

Findings

Derived Bethe ansatz equations for boundary affine Yangian models

Provided three solutions to the Sklyanin KRKR equation

Connected affine Yangian structures with BCD conformal field theories

Abstract

In these notes we study integrable structures of conformal field theory with $\textrm{BCD}$ symmetry. We realise these integrable structures as affine Yangian $\mathfrak{gl}(1)$ "spin chains" with boundaries. We provide three solutions of Sklyanin $\textrm{KRKR}$ equation compatible with affine Yangian $R$-matrix and derive Bethe ansatz equations for the spectrum.