Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian
Alexey Litvinov (Center for Advanced Studies, Skolkovo Institute of Science and Technology, 1 Nobel Street, Moscow, 143026, Russia, Landau Institute for Theoretical Physics, Akademika Semenova av. 1A, Chernogolovka, 142432, Russia); Ilya Vilkoviskiy (Center for Advanced Studies, Skolkovo Institute of Science and Technology, 1 Nobel Street, Moscow, 143026, Russia, Faculty of Mathematics, National Research University Higher School of Economics, Usacheva 6, Moscow, 119048, Russia)
In these notes we study integrable structures of conformal field theory with BCD symmetry. We realise these integrable structures as $$ \mathfrak{gl} $$ (1) affine Yangian “spin chains” with boundaries. We provide three solutions of Sklyanin KRKR equation compatible with the affine Yangian R-matrix and derive Bethe ansatz equations for the spectrum. Our analysis provides a unified approach to the integrable structures with BCD symmetry including superalgebras.
