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

Abstract

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

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• ABCD of qq-characters
• Gauge origami and quiver W-algebras
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• An Overview of Crystals and Double Quiver Yangians
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• The ODE/IM Correspondence between $C(2{)}^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT